



\section{Appendix}\label{sec_app}
In each of the subsections below we give generators of the group in its
permutation representation, followed by the set of orbits used for a block
of the design. This orbited under the group generated by the given orbits
and either the binary code from this design or the hull of the code will
be the code we have discussed in the paper.
\subsection{$J_1$ of degree 1045: $[1045,20,456]_2$}
{\small
\begin{verbatim}
Generators(a2);
[
    (1, 3, 6)(2, 4, 8)(5, 9, 14)(7, 11, 16)(12, 17, 22)(13, 18, 24)(15, 19, 
        25)(20, 26, 33)(21, 27, 35)(23, 29, 38)(28, 36, 37)(30, 39, 48)(31, 40,
        50)(32, 41, 52)(34, 43, 55)(42, 53, 54)(44, 56, 68)(45, 57, 70)(46, 58,
        72)(47, 59, 74)(49, 61, 77)(51, 63, 80)(60, 75, 76)(62, 78, 79)(64, 81,
        97)(65, 82, 99)(66, 83, 101)(67, 84, 103)(69, 86, 106)(71, 88, 109)(73,
        90, 112)(85, 104, 105)(87, 107, 129)(89, 110, 111)(91, 113, 135)(92, 
        114, 137)(93, 115, 139)(94, 116, 141)(95, 117, 143)(96, 118, 145)(98, 
        120, 148)(100, 122, 151)(102, 124, 154)(108, 130, 159)(119, 146, 
        147)(121, 149, 178)(123, 152, 153)(125, 155, 184)(126, 156, 186)(127, 
        157, 188)(128, 158, 190)(131, 160, 193)(132, 161, 195)(133, 162, 
        164)(134, 163, 196)(136, 165, 183)(138, 167, 199)(140, 169, 202)(142, 
        171, 205)(144, 173, 208)(150, 179, 213)(166, 197, 230)(168, 200, 
        201)(170, 203, 236)(172, 206, 207)(174, 209, 242)(175, 210, 244)(176, 
        211, 246)(177, 212, 248)(180, 214, 251)(181, 215, 253)(182, 216, 
        229)(185, 218, 256)(187, 220, 259)(189, 222, 262)(191, 224, 265)(192, 
        225, 267)(194, 227, 270)(198, 231, 271)(204, 237, 276)(217, 228, 
        255)(219, 257, 296)(221, 260, 261)(223, 263, 302)(226, 268, 269)(232, 
        272, 311)(233, 273, 313)(234, 274, 315)(235, 275, 317)(238, 277, 
        320)(239, 278, 322)(240, 279, 324)(241, 280, 326)(243, 282, 329)(245, 
        284, 332)(247, 286, 335)(249, 288, 338)(250, 289, 340)(252, 291, 
        343)(254, 293, 346)(258, 297, 349)(264, 303, 355)(266, 305, 358)(281, 
        327, 328)(283, 330, 383)(285, 333, 334)(287, 336, 375)(290, 341, 
        342)(292, 344, 395)(294, 347, 399)(295, 348, 392)(298, 339, 390)(299, 
        350, 403)(300, 351, 405)(301, 352, 407)(304, 356, 357)(306, 359, 
        413)(307, 360, 415)(308, 361, 417)(309, 362, 419)(310, 363, 421)(312, 
        365, 424)(314, 367, 427)(316, 369, 430)(318, 371, 433)(319, 372, 
        435)(321, 374, 337)(323, 376, 439)(325, 378, 442)(331, 384, 445)(345, 
        396, 454)(353, 408, 354)(364, 422, 423)(366, 425, 481)(368, 428, 
        429)(370, 431, 486)(373, 436, 437)(377, 440, 441)(379, 443, 496)(380, 
        444, 382)(385, 446, 500)(386, 447, 502)(387, 448, 504)(388, 449, 
        438)(389, 450, 451)(391, 452, 401)(393, 453, 508)(397, 455, 510)(398, 
        456, 511)(400, 458, 513)(402, 459, 514)(404, 461, 517)(406, 463, 
        520)(409, 466, 524)(410, 467, 526)(411, 468, 528)(412, 469, 530)(414, 
        471, 533)(416, 473, 536)(418, 474, 537)(420, 476, 540)(426, 482, 
        545)(432, 487, 551)(434, 489, 554)(457, 501, 512)(460, 515, 573)(462, 
        518, 519)(464, 521, 579)(465, 522, 581)(470, 531, 532)(472, 534, 
        593)(475, 538, 539)(477, 541, 599)(478, 542, 601)(479, 543, 602)(480, 
        544, 603)(483, 546, 606)(484, 547, 608)(485, 548, 609)(488, 552, 
        553)(490, 555, 614)(491, 556, 616)(492, 557, 589)(493, 558, 619)(494, 
        559, 621)(495, 560, 623)(497, 562, 626)(498, 563, 628)(499, 564, 
        507)(503, 566, 632)(505, 568, 635)(509, 569, 637)(516, 574, 620)(523, 
        582, 649)(525, 584, 652)(527, 586, 655)(529, 588, 618)(535, 594, 
        659)(549, 610, 550)(561, 624, 625)(565, 630, 686)(567, 633, 634)(570, 
        638, 693)(571, 639, 694)(572, 640, 696)(575, 641, 697)(576, 642, 
        699)(577, 643, 587)(578, 644, 700)(580, 646, 703)(583, 650, 651)(585, 
        653, 710)(590, 656, 713)(591, 657, 715)(592, 658, 717)(595, 660, 
        720)(596, 613, 674)(597, 661, 722)(598, 662, 724)(600, 664, 721)(604, 
        668, 730)(607, 670, 733)(611, 672, 735)(612, 673, 737)(615, 676, 
        740)(617, 677, 742)(622, 679, 745)(627, 682, 749)(629, 684, 636)(631, 
        687, 753)(645, 701, 702)(647, 704, 764)(648, 705, 765)(654, 711, 
        769)(663, 725, 726)(665, 727, 779)(667, 728, 780)(669, 731, 732)(671, 
        734, 783)(675, 738, 739)(678, 743, 744)(680, 746, 792)(681, 747, 
        748)(683, 750, 751)(685, 752, 796)(688, 754, 799)(689, 755, 801)(690, 
        756, 803)(691, 757, 805)(692, 758, 807)(695, 760, 759)(706, 719, 
        774)(707, 766, 813)(708, 767, 815)(709, 768, 817)(712, 770, 819)(714, 
        772, 822)(718, 773, 824)(723, 777, 829)(729, 781, 832)(736, 785, 
        835)(741, 789, 838)(761, 808, 854)(762, 809, 855)(763, 810, 857)(771, 
        820, 866)(775, 826, 806)(776, 827, 828)(778, 818, 864)(782, 791, 
        840)(784, 833, 834)(786, 831, 830)(787, 836, 875)(788, 837, 853)(790, 
        839, 878)(793, 842, 882)(794, 843, 869)(795, 844, 884)(797, 816, 
        862)(798, 846, 814)(800, 848, 888)(802, 850, 891)(804, 851, 893)(811, 
        858, 898)(812, 859, 900)(821, 867, 906)(823, 868, 883)(825, 870, 
        899)(841, 880, 917)(845, 885, 922)(847, 860, 887)(849, 889, 926)(852, 
        894, 931)(856, 896, 934)(861, 901, 902)(863, 903, 937)(865, 905, 
        940)(871, 907, 942)(872, 908, 944)(873, 909, 916)(874, 910, 947)(876, 
        912, 950)(877, 913, 952)(879, 915, 955)(881, 918, 956)(886, 923, 
        959)(890, 927, 951)(892, 920, 958)(895, 932, 933)(897, 935, 941)(904, 
        938, 943)(911, 948, 974)(914, 953, 979)(919, 957, 936)(921, 930, 
        962)(924, 960, 987)(925, 961, 964)(929, 949, 975)(939, 968, 981)(945, 
        972, 995)(946, 971, 994)(954, 980, 998)(963, 990, 977)(965, 991, 
        984)(966, 992, 967)(969, 993, 970)(976, 996, 1010)(978, 997, 1011)(982,
        999, 1014)(983, 1000, 986)(985, 1001, 1016)(988, 1003, 1019)(989, 1004,
        1020)(1002, 1017, 1018)(1005, 1021, 1009)(1006, 1022, 1032)(1007, 1023,
        1034)(1008, 1024, 1035)(1012, 1026, 1031)(1013, 1027, 1037)(1015, 1029,
        1040)(1025, 1036, 1044)(1028, 1038, 1039)(1030, 1041, 1043)(1033, 1042,
        1045),
    (1, 2)(3, 5)(4, 7)(6, 10)(8, 12)(9, 13)(11, 15)(14, 19)(16, 20)(17, 21)(18,
        23)(22, 28)(24, 30)(25, 31)(26, 32)(27, 34)(29, 37)(33, 42)(35, 44)(36,
        45)(38, 46)(39, 47)(40, 49)(41, 51)(43, 54)(48, 60)(50, 62)(52, 64)(53,
        65)(55, 66)(56, 67)(57, 69)(58, 71)(59, 73)(61, 76)(63, 79)(68, 85)(70,
        87)(72, 89)(74, 91)(75, 92)(77, 93)(78, 94)(80, 95)(81, 96)(82, 98)(83,
        100)(84, 102)(86, 105)(88, 108)(90, 111)(97, 119)(99, 121)(101, 
        123)(103, 125)(104, 126)(106, 127)(107, 128)(109, 131)(110, 132)(112, 
        133)(113, 134)(114, 136)(115, 138)(116, 140)(117, 142)(118, 144)(120, 
        147)(122, 150)(124, 153)(129, 130)(135, 164)(137, 166)(139, 168)(141, 
        170)(143, 172)(145, 174)(146, 175)(148, 176)(149, 177)(151, 180)(152, 
        181)(154, 182)(155, 183)(156, 185)(157, 187)(158, 189)(159, 191)(160, 
        192)(161, 194)(162, 165)(163, 196)(167, 198)(169, 201)(171, 204)(173, 
        207)(178, 179)(184, 217)(186, 219)(188, 221)(190, 223)(193, 226)(195, 
        228)(197, 229)(199, 232)(200, 233)(202, 234)(203, 235)(205, 238)(206, 
        239)(208, 240)(209, 241)(210, 243)(211, 245)(212, 247)(213, 249)(214, 
        250)(215, 252)(216, 254)(218, 255)(220, 258)(222, 261)(224, 264)(225, 
        266)(227, 269)(230, 231)(236, 237)(242, 281)(244, 283)(246, 285)(248, 
        287)(251, 290)(253, 292)(256, 294)(257, 295)(259, 298)(260, 299)(262, 
        300)(263, 301)(265, 304)(267, 306)(268, 307)(270, 308)(271, 309)(272, 
        310)(273, 312)(274, 314)(275, 316)(276, 318)(277, 319)(278, 321)(279, 
        323)(280, 325)(282, 328)(284, 331)(286, 334)(288, 337)(289, 339)(291, 
        342)(293, 345)(296, 297)(302, 353)(303, 354)(305, 357)(311, 364)(313, 
        366)(315, 368)(317, 370)(320, 373)(322, 375)(324, 377)(326, 379)(327, 
        380)(329, 381)(330, 382)(332, 385)(333, 386)(335, 387)(336, 388)(338, 
        389)(340, 391)(341, 392)(343, 393)(344, 394)(346, 397)(347, 398)(348, 
        400)(349, 401)(350, 402)(351, 404)(352, 406)(355, 409)(356, 410)(358, 
        411)(359, 412)(360, 414)(361, 416)(362, 418)(363, 420)(365, 423)(367, 
        426)(369, 429)(371, 432)(372, 434)(374, 437)(376, 438)(378, 441)(383, 
        384)(390, 451)(395, 396)(399, 457)(403, 460)(405, 462)(407, 464)(408, 
        465)(413, 470)(415, 472)(417, 456)(419, 475)(421, 477)(422, 478)(424, 
        479)(425, 480)(427, 483)(428, 484)(431, 485)(433, 488)(435, 490)(436, 
        491)(439, 492)(440, 493)(442, 494)(443, 495)(444, 497)(445, 498)(446, 
        499)(447, 501)(448, 503)(449, 505)(450, 459)(452, 506)(453, 507)(454, 
        508)(455, 509)(458, 512)(461, 516)(463, 519)(466, 523)(467, 525)(468, 
        527)(469, 529)(471, 532)(473, 535)(474, 510)(476, 539)(481, 482)(486, 
        549)(487, 550)(489, 553)(496, 561)(500, 513)(502, 565)(504, 567)(511, 
        570)(514, 571)(515, 572)(517, 575)(518, 576)(520, 577)(521, 578)(522, 
        580)(524, 583)(526, 585)(528, 587)(530, 589)(531, 590)(533, 591)(534, 
        592)(536, 595)(537, 555)(538, 596)(540, 597)(541, 598)(542, 600)(543, 
        544)(545, 604)(546, 605)(547, 607)(548, 608)(551, 611)(552, 612)(554, 
        613)(556, 615)(557, 617)(558, 618)(559, 620)(560, 622)(562, 625)(563, 
        627)(564, 629)(566, 631)(568, 634)(569, 636)(573, 574)(579, 645)(581, 
        647)(582, 648)(584, 651)(586, 654)(588, 643)(593, 594)(599, 663)(601, 
        665)(602, 666)(603, 667)(606, 669)(609, 623)(610, 671)(614, 675)(616, 
        639)(619, 641)(621, 678)(624, 680)(626, 681)(628, 683)(630, 685)(632, 
        688)(633, 689)(635, 690)(637, 691)(638, 692)(640, 695)(642, 698)(644, 
        655)(646, 702)(649, 706)(650, 707)(652, 708)(653, 709)(656, 712)(657, 
        714)(658, 716)(659, 718)(660, 719)(661, 721)(662, 723)(664, 726)(668, 
        729)(670, 732)(672, 701)(673, 736)(674, 727)(676, 739)(677, 741)(679, 
        744)(682, 748)(684, 751)(686, 687)(693, 752)(694, 759)(696, 761)(697, 
        699)(700, 724)(703, 762)(704, 763)(705, 764)(710, 711)(713, 771)(715, 
        717)(720, 775)(722, 776)(725, 778)(728, 779)(730, 731)(733, 746)(734, 
        782)(735, 784)(737, 786)(738, 787)(740, 788)(742, 770)(743, 790)(745, 
        791)(747, 793)(749, 794)(750, 795)(753, 797)(754, 798)(755, 800)(756, 
        802)(757, 804)(758, 806)(765, 811)(766, 812)(767, 814)(768, 816)(769, 
        818)(772, 821)(773, 823)(774, 825)(777, 828)(780, 830)(781, 831)(783, 
        809)(785, 834)(789, 803)(792, 841)(796, 845)(799, 847)(801, 849)(805, 
        836)(807, 852)(808, 853)(810, 856)(813, 860)(815, 861)(817, 863)(819, 
        865)(820, 858)(822, 868)(824, 869)(826, 871)(827, 872)(829, 833)(832, 
        873)(835, 874)(837, 876)(838, 877)(839, 854)(840, 879)(842, 881)(843, 
        870)(844, 883)(846, 886)(848, 887)(850, 890)(851, 892)(855, 895)(857, 
        897)(859, 899)(862, 902)(864, 904)(866, 867)(875, 911)(878, 914)(880, 
        916)(882, 919)(884, 920)(885, 921)(888, 924)(889, 925)(891, 928)(893, 
        929)(894, 930)(896, 933)(898, 907)(900, 936)(901, 923)(903, 922)(905, 
        939)(906, 941)(908, 943)(909, 945)(910, 946)(912, 949)(913, 951)(915, 
        954)(917, 918)(926, 927)(932, 963)(934, 964)(935, 965)(937, 966)(938, 
        967)(940, 969)(942, 970)(944, 971)(947, 972)(948, 973)(950, 976)(952, 
        977)(953, 978)(955, 981)(956, 982)(957, 983)(958, 984)(959, 985)(960, 
        986)(961, 988)(962, 989)(968, 990)(974, 975)(979, 980)(987, 1002)(991, 
        1005)(992, 1006)(993, 1004)(994, 1007)(995, 1008)(996, 1009)(997, 
        1010)(998, 1012)(999, 1013)(1000, 1015)(1001, 1016)(1003, 1018)(1011, 
        1025)(1014, 1028)(1017, 1030)(1019, 1021)(1020, 1031)(1022, 1026)(1023,
        1033)(1027, 1035)(1029, 1039)(1032, 1042)(1034, 1037)(1036, 1043)(1038,
        1041)(1044, 1045)
]
orbs[1],orbs[3],orbs[5],orbs[10],orbs[11];
GSet{@ 1 @}
GSet{@ 31, 751, 80, 249, 83, 298, 875, 35, 514, 509, 220, 243, 108, 260, 904, 
823, 69, 269, 303, 116, 534, 356, 958, 828, 851, 471, 42, 994 @}
GSet{@ 74, 781, 587, 583, 746, 855, 359, 683, 723, 398, 162, 335, 767, 560, 
624, 530, 791, 507, 395, 426, 832, 626, 203, 637, 933, 732, 193, 619, 777, 89, 
919, 79, 611, 526, 305, 667, 758, 796, 379, 663, 241, 717, 599, 813, 825, 601, 
578, 877, 447, 981, 176, 835, 550, 612, 169, 722 @}
GSet{@ 20, 182, 588, 815, 648, 805, 23, 826, 545, 222, 883, 489, 478, 163, 897,
1034, 584, 677, 707, 422, 739, 107, 1022, 347, 55, 239, 866, 914, 348, 541, 
961, 86, 124, 92, 73, 416, 311, 363, 963, 1026, 743, 923, 544, 173, 951, 68, 
413, 678, 555, 399, 37, 735, 492, 133, 476, 798, 715, 771, 289, 308, 516, 942, 
189, 412, 336, 496, 443, 97, 949, 179, 691, 679, 799, 749, 323, 1036, 867, 290,
242, 1025, 110, 138, 47, 334, 653, 217, 774, 843, 349, 192, 579, 753, 100, 527,
82, 446, 126, 497, 357, 178, 386, 129, 209, 346, 88, 485, 183, 186, 227, 271, 
976, 320, 246, 955, 531, 525, 341, 253, 780, 113, 598, 111, 101, 469, 48, 393, 
263, 703, 155, 453, 630, 214, 688, 255, 741, 948, 464, 681, 286, 890, 863, 901,
920, 449, 292, 1006, 177, 325, 689, 623, 512, 233, 91, 822, 752, 461, 888, 943,
842, 596, 638, 518, 90, 628, 384, 840, 979, 378 @}
GSet{@ 34, 642, 811, 931, 1023, 939, 276, 212, 905, 345, 711, 591, 221, 766, 
130, 170, 868, 614, 145, 566, 382, 792, 482, 428, 152, 941, 947, 900, 312, 895,
829, 669, 50, 300, 762, 213, 925, 247, 620, 706, 1035, 922, 617, 45, 597, 115, 
806, 66, 593, 894, 608, 859, 969, 652, 857, 834, 700, 72, 659, 693, 945, 872, 
893, 419, 915, 410, 123, 159, 980, 342, 561, 768, 1004, 911, 397, 165, 528, 
968, 216, 205, 275, 633, 409, 477, 794, 367, 65, 510, 603, 639, 610, 405, 658, 
235, 122, 148, 666, 804, 535, 783, 574, 499, 158, 750, 94, 769, 990, 140, 882, 
520, 76, 716, 64, 869, 451, 776, 307, 712, 190, 654, 548, 999, 458, 403, 938, 
682, 252, 887, 60, 993, 721, 296, 279, 841, 299, 747, 651, 757, 622, 640, 315, 
724, 782, 892, 331, 371, 1021, 1037, 908, 154, 818, 713, 934, 160, 641, 795, 
172, 546, 950, 351, 775, 965, 726, 629, 210, 215, 197, 103 @}
\end{verbatim}}
\subsection{$J_1$ of degree 1463: $[1463,20,608]_2$}
{\small
\begin{verbatim}
> Generators(a2);
{
    (1, 2)(3, 12)(4, 19)(5, 25)(6, 28)(7, 35)(8, 42)(9, 49)(10, 56)(11, 62)(13,
        74)(14, 79)(15, 86)(16, 93)(17, 100)(18, 106)(20, 118)(21, 125)(22, 
        129)(23, 131)(24, 133)(26, 139)(27, 145)(29, 152)(30, 156)(31, 163)(32,
        170)(33, 177)(34, 107)(36, 194)(37, 201)(38, 207)(39, 213)(40, 220)(41,
        226)(43, 236)(44, 241)(45, 247)(46, 254)(47, 260)(48, 265)(50, 277)(51,
        283)(52, 289)(53, 296)(54, 303)(57, 78)(59, 328)(60, 334)(61, 340)(63, 
        128)(64, 352)(65, 356)(66, 361)(67, 132)(68, 72)(69, 370)(70, 377)(71, 
        383)(73, 390)(75, 397)(76, 402)(77, 407)(80, 418)(81, 424)(82, 255)(83,
        275)(84, 354)(85, 181)(87, 450)(88, 456)(89, 461)(90, 466)(91, 469)(92,
        474)(94, 481)(95, 488)(96, 276)(97, 496)(98, 500)(99, 501)(101, 
        503)(102, 502)(103, 509)(104, 512)(105, 514)(108, 525)(109, 142)(110, 
        530)(111, 305)(112, 204)(113, 538)(114, 182)(115, 546)(116, 232)(117, 
        553)(119, 560)(120, 566)(121, 345)(122, 421)(123, 582)(124, 470)(126, 
        595)(127, 597)(130, 602)(134, 368)(135, 619)(136, 622)(137, 429)(138, 
        628)(140, 635)(141, 638)(143, 648)(144, 652)(146, 658)(147, 664)(148, 
        670)(149, 498)(150, 660)(151, 679)(153, 688)(154, 692)(155, 696)(157, 
        704)(158, 705)(159, 188)(160, 711)(161, 552)(162, 716)(164, 239)(165, 
        726)(166, 171)(167, 733)(168, 237)(169, 331)(172, 752)(173, 757)(174, 
        760)(175, 729)(176, 697)(178, 492)(179, 773)(180, 406)(183, 787)(184, 
        451)(185, 203)(186, 758)(187, 799)(189, 803)(190, 809)(191, 815)(192, 
        372)(193, 598)(195, 828)(196, 831)(197, 837)(198, 262)(199, 843)(200, 
        845)(202, 385)(205, 858)(206, 859)(208, 864)(209, 867)(210, 788)(211, 
        751)(212, 872)(214, 876)(215, 882)(216, 885)(218, 892)(219, 894)(221, 
        426)(222, 900)(223, 902)(224, 725)(225, 907)(227, 914)(229, 922)(230, 
        273)(231, 928)(233, 931)(234, 932)(235, 935)(238, 942)(240, 261)(242, 
        778)(243, 958)(244, 825)(245, 774)(246, 893)(248, 968)(249, 970)(250, 
        795)(251, 587)(252, 359)(253, 978)(256, 982)(257, 984)(258, 320)(259, 
        987)(263, 997)(264, 1000)(266, 462)(267, 686)(268, 926)(269, 663)(270, 
        526)(271, 507)(272, 1013)(278, 1030)(279, 1036)(280, 959)(281, 
        615)(282, 612)(284, 1041)(285, 349)(286, 1048)(287, 839)(288, 
        1052)(290, 294)(291, 645)(292, 708)(293, 1062)(295, 952)(297, 
        1069)(298, 1070)(299, 1072)(300, 1075)(301, 1031)(302, 852)(304, 
        1081)(306, 449)(308, 594)(309, 917)(310, 1091)(311, 542)(312, 315)(313,
        640)(314, 562)(316, 1098)(317, 703)(318, 558)(319, 1102)(321, 478)(322,
        1112)(323, 344)(324, 949)(325, 1115)(326, 603)(327, 610)(329, 
        1119)(330, 1044)(332, 1122)(333, 731)(335, 338)(336, 1128)(337, 
        360)(339, 1014)(341, 613)(342, 411)(343, 1140)(346, 1143)(347, 
        980)(348, 880)(350, 1057)(351, 950)(353, 1149)(355, 797)(357, 689)(358,
        1038)(362, 903)(363, 1159)(364, 934)(365, 653)(366, 1163)(367, 
        681)(371, 1168)(373, 1172)(374, 693)(375, 1179)(376, 833)(378, 
        1099)(379, 447)(380, 472)(381, 897)(382, 1117)(384, 699)(386, 
        1028)(387, 685)(388, 1196)(389, 455)(391, 414)(392, 836)(393, 
        1204)(394, 596)(395, 1205)(396, 1208)(398, 400)(399, 1213)(401, 
        1215)(403, 439)(404, 1219)(405, 992)(408, 1165)(409, 1134)(410, 
        1169)(412, 742)(413, 1226)(415, 855)(416, 747)(417, 814)(419, 
        1116)(420, 1071)(422, 953)(423, 1008)(425, 623)(427, 1073)(428, 
        1078)(430, 929)(431, 591)(433, 495)(434, 1241)(435, 798)(436, 650)(437,
        1240)(438, 1244)(440, 1184)(441, 453)(442, 1246)(443, 1090)(444, 
        608)(445, 694)(446, 1100)(448, 605)(452, 1152)(454, 1074)(457, 
        857)(458, 1256)(459, 777)(460, 870)(463, 790)(464, 1257)(465, 611)(467,
        740)(468, 812)(471, 1206)(473, 1231)(475, 1267)(476, 510)(477, 
        1262)(479, 555)(480, 1158)(482, 722)(483, 983)(485, 1276)(486, 
        1277)(487, 631)(489, 723)(490, 1185)(491, 1286)(493, 1289)(494, 
        874)(497, 816)(499, 1292)(504, 793)(505, 661)(506, 565)(508, 607)(511, 
        1255)(513, 1025)(515, 1304)(516, 1250)(517, 1265)(518, 951)(519, 
        963)(520, 739)(521, 715)(522, 762)(523, 1314)(524, 1171)(527, 
        1317)(528, 1133)(529, 1045)(531, 1108)(532, 656)(533, 966)(534, 
        1258)(535, 1065)(536, 1324)(537, 1221)(539, 869)(540, 1058)(541, 
        600)(543, 1239)(545, 556)(547, 1336)(548, 1155)(549, 1339)(550, 
        564)(551, 659)(554, 834)(557, 585)(559, 1105)(561, 1095)(563, 
        1261)(567, 687)(568, 846)(569, 1316)(570, 719)(571, 630)(572, 
        1352)(573, 1355)(574, 1357)(575, 1359)(576, 1360)(578, 1300)(579, 
        1361)(580, 1363)(581, 1141)(583, 724)(584, 1341)(586, 1103)(588, 
        820)(589, 1162)(590, 889)(592, 868)(593, 721)(599, 1381)(601, 955)(604,
        1223)(606, 1147)(609, 1222)(614, 1389)(616, 1299)(617, 1347)(618, 
        1249)(620, 1393)(621, 750)(624, 1076)(625, 962)(626, 1373)(629, 
        1397)(632, 1399)(633, 973)(634, 1209)(636, 1061)(637, 807)(639, 
        1406)(641, 1180)(642, 1123)(643, 1104)(644, 667)(646, 1371)(647, 
        1087)(649, 1229)(651, 1410)(654, 1064)(655, 1027)(657, 1237)(662, 
        1271)(666, 1407)(668, 1212)(669, 921)(671, 1418)(672, 977)(673, 
        853)(674, 1252)(675, 1320)(676, 1368)(677, 767)(678, 1313)(680, 
        920)(682, 1019)(683, 1379)(684, 779)(690, 707)(691, 1227)(695, 
        1236)(698, 706)(700, 1247)(701, 1191)(702, 1335)(709, 995)(710, 
        1238)(712, 947)(713, 1398)(714, 1328)(717, 1007)(718, 1043)(720, 
        1315)(727, 1268)(728, 957)(730, 1295)(732, 1340)(734, 1307)(736, 
        786)(737, 915)(738, 768)(741, 1345)(743, 964)(744, 1173)(745, 
        1082)(746, 863)(748, 943)(749, 829)(753, 1287)(754, 785)(755, 
        1301)(756, 1401)(759, 954)(761, 1012)(763, 1002)(764, 999)(765, 
        1068)(766, 1326)(769, 1049)(770, 1132)(771, 939)(772, 823)(775, 
        1416)(776, 1426)(780, 887)(781, 838)(782, 1282)(783, 1224)(784, 
        1442)(789, 981)(791, 1283)(792, 1278)(794, 1365)(796, 1251)(800, 
        1170)(801, 1136)(802, 1198)(804, 1430)(805, 1414)(806, 871)(808, 
        1089)(810, 1334)(811, 899)(813, 1009)(817, 976)(818, 1114)(819, 
        946)(821, 1055)(822, 1420)(824, 1199)(826, 1284)(827, 1050)(830, 
        996)(832, 1203)(835, 1201)(840, 1423)(841, 1439)(844, 944)(847, 
        1417)(848, 1146)(849, 1353)(850, 974)(851, 1026)(854, 1434)(856, 
        1154)(860, 1217)(861, 1321)(862, 1310)(865, 1337)(866, 1358)(873, 
        1306)(875, 1424)(877, 989)(878, 1003)(879, 1370)(881, 1455)(883, 
        1273)(884, 1195)(886, 888)(890, 1288)(891, 1457)(895, 1269)(896, 
        1193)(898, 1445)(901, 1242)(904, 1157)(905, 1127)(906, 1356)(908, 
        912)(909, 1431)(910, 1453)(911, 1280)(913, 1216)(916, 1415)(919, 
        1130)(923, 1344)(924, 971)(925, 1093)(927, 986)(930, 1225)(933, 
        940)(936, 1161)(937, 1106)(941, 988)(945, 1380)(948, 1458)(956, 
        1409)(961, 1362)(965, 1230)(967, 1015)(969, 1378)(972, 1092)(975, 
        1384)(979, 1211)(985, 1425)(990, 1388)(991, 1018)(993, 1412)(994, 
        1270)(998, 1460)(1001, 1235)(1004, 1342)(1005, 1354)(1006, 1279)(1010, 
        1232)(1011, 1309)(1016, 1391)(1017, 1254)(1020, 1034)(1021, 1086)(1022,
        1121)(1023, 1290)(1024, 1374)(1029, 1429)(1032, 1448)(1033, 1312)(1035,
        1164)(1037, 1403)(1039, 1200)(1040, 1437)(1042, 1190)(1046, 1151)(1047,
        1451)(1051, 1450)(1053, 1260)(1056, 1145)(1059, 1228)(1060, 1233)(1063,
        1382)(1066, 1375)(1067, 1275)(1077, 1188)(1079, 1182)(1080, 1189)(1084,
        1446)(1085, 1394)(1088, 1187)(1094, 1156)(1096, 1323)(1101, 1138)(1107,
        1264)(1109, 1427)(1110, 1302)(1111, 1449)(1113, 1311)(1118, 1125)(1120,
        1331)(1124, 1308)(1129, 1390)(1131, 1463)(1135, 1325)(1137, 1461)(1139,
        1266)(1142, 1220)(1144, 1438)(1148, 1192)(1153, 1404)(1160, 1428)(1166,
        1332)(1167, 1377)(1174, 1338)(1175, 1419)(1176, 1364)(1177, 1298)(1181,
        1462)(1183, 1456)(1186, 1234)(1194, 1197)(1207, 1459)(1214, 1452)(1218,
        1395)(1245, 1408)(1248, 1400)(1253, 1330)(1259, 1293)(1263, 1454)(1272,
        1441)(1274, 1351)(1281, 1392)(1285, 1366)(1294, 1387)(1296, 1383)(1297,
        1318)(1303, 1435)(1305, 1421)(1319, 1376)(1322, 1343)(1327, 1440)(1333,
        1444)(1346, 1433)(1348, 1372)(1367, 1405)(1369, 1411)(1385, 1422)(1386,
        1443)(1396, 1447)(1402, 1436)(1413, 1432),
    (1, 3, 13)(2, 6, 29)(4, 20, 119)(5, 26, 82)(7, 36, 195)(8, 43, 237)(9, 50, 
        278)(10, 57, 21)(11, 63, 349)(12, 69, 371)(14, 80, 419)(15, 87, 
        451)(16, 94, 482)(17, 101, 437)(18, 107, 522)(19, 112, 532)(22, 130, 
        372)(23, 132, 72)(24, 134, 569)(25, 135, 117)(27, 146, 324)(28, 147, 
        665)(30, 157, 579)(31, 164, 722)(32, 171, 203)(33, 178, 771)(34, 182, 
        784)(35, 188, 279)(37, 202, 850)(38, 208, 865)(39, 214, 243)(40, 221, 
        354)(41, 227, 440)(42, 230, 47)(44, 242, 955)(45, 248, 969)(46, 255, 
        517)(48, 266, 65)(49, 272, 1014)(51, 284, 1042)(52, 290, 365)(53, 297, 
        534)(54, 304, 205)(55, 307, 1085)(56, 312, 150)(58, 322, 1109)(59, 329,
        1044)(60, 335, 905)(61, 341, 506)(62, 345, 1105)(64, 234, 933)(66, 362,
        659)(67, 291, 682)(68, 105, 515)(70, 378, 1185)(71, 384, 1192)(73, 391,
        1201)(74, 393, 1203)(75, 398, 979)(76, 403, 1218)(77, 408, 1067)(78, 
        414, 320)(79, 160, 712)(81, 425, 1234)(83, 433, 565)(84, 436, 648)(85, 
        373, 949)(86, 444, 588)(88, 457, 192)(89, 245, 962)(90, 467, 903)(91, 
        470, 1024)(92, 475, 1268)(93, 446, 265)(95, 489, 676)(96, 492, 921)(97,
        497, 450)(98, 223, 900)(99, 502, 1271)(100, 432, 396)(102, 194, 
        187)(103, 510, 907)(104, 513, 1285)(106, 309, 110)(108, 526, 1316)(109,
        409, 762)(111, 531, 984)(113, 539, 1154)(114, 256, 837)(115, 232, 
        747)(116, 550, 909)(118, 555, 1033)(120, 567, 1348)(121, 281, 810)(122,
        185, 794)(123, 583, 1107)(124, 585, 1366)(125, 590, 609)(126, 596, 
        1294)(127, 598, 871)(128, 599, 222)(129, 162, 315)(131, 605, 820)(133, 
        614, 416)(136, 623, 201)(137, 624, 1150)(138, 458, 405)(139, 633, 
        1046)(140, 589, 878)(141, 639, 1395)(142, 644, 1411)(143, 649, 
        1013)(144, 653, 1248)(145, 657, 824)(148, 342, 1139)(149, 673, 
        861)(151, 680, 915)(152, 683, 1167)(153, 689, 1392)(154, 693, 663)(155,
        697, 681)(156, 200, 846)(158, 706, 1307)(159, 270, 215)(161, 568, 
        1324)(163, 382, 1190)(165, 727, 899)(166, 728, 966)(167, 734, 845)(168,
        739, 801)(169, 452, 1031)(170, 549, 904)(172, 566, 998)(173, 758, 
        1338)(174, 607, 1018)(175, 763, 870)(176, 494, 898)(177, 334, 686)(179,
        774, 1025)(180, 296, 443)(181, 407, 632)(183, 788, 684)(184, 343, 
        817)(186, 530, 911)(189, 804, 857)(190, 780, 574)(191, 816, 942)(193, 
        206, 860)(196, 832, 947)(197, 838, 1429)(198, 660, 1416)(199, 275, 
        1020)(204, 856, 636)(207, 578, 688)(209, 311, 367)(210, 347, 383)(211, 
        570, 503)(212, 873, 884)(213, 523, 964)(216, 353, 377)(217, 888, 
        1446)(218, 893, 679)(219, 895, 1447)(220, 718, 643)(224, 350, 896)(225,
        687, 1282)(226, 908, 753)(228, 920, 1081)(229, 631, 1365)(231, 929, 
        924)(233, 703, 1135)(235, 936, 535)(236, 269, 239)(238, 943, 813)(240, 
        928, 809)(241, 662, 830)(244, 344, 1142)(246, 732, 729)(247, 965, 
        1425)(249, 386, 677)(250, 339, 1133)(251, 972, 1126)(252, 800, 
        902)(253, 840, 263)(254, 968, 876)(257, 985, 789)(258, 986, 593)(259, 
        988, 1236)(260, 990, 937)(261, 552, 1094)(262, 658, 1214)(264, 1001, 
        1204)(267, 1007, 1310)(268, 1008, 591)(271, 454, 1238)(273, 1016, 
        1118)(274, 474, 650)(276, 413, 1227)(277, 1026, 1458)(280, 1037, 
        560)(282, 1038, 374)(283, 1040, 287)(285, 1047, 715)(286, 1049, 
        1061)(288, 726, 360)(289, 1053, 1368)(292, 582, 711)(293, 1063, 
        422)(294, 557, 951)(295, 584, 1251)(298, 1071, 461)(299, 615, 337)(300,
        1076, 970)(301, 411, 637)(302, 1051, 634)(303, 1078, 1029)(305, 314, 
        1097)(306, 1083, 692)(308, 638, 1098)(310, 586, 1337)(313, 778, 
        424)(316, 554, 1326)(317, 867, 1130)(318, 710, 1189)(319, 479, 
        1269)(321, 702, 1231)(323, 595, 807)(325, 1116, 953)(326, 401, 
        359)(327, 1117, 803)(328, 721, 553)(330, 1064, 889)(331, 417, 
        1015)(332, 1004, 925)(333, 592, 498)(336, 518, 1173)(338, 1132, 
        1145)(340, 797, 472)(346, 1144, 491)(348, 1146, 1349)(351, 786, 
        811)(352, 855, 1370)(355, 843, 1062)(356, 694, 395)(357, 1153, 
        1213)(358, 1155, 1100)(361, 818, 1059)(363, 620, 669)(364, 1160, 
        600)(366, 1164, 1156)(368, 1165, 775)(369, 699, 1339)(370, 1131, 
        1000)(375, 1124, 731)(376, 960, 756)(379, 890, 946)(380, 1188, 
        826)(381, 1114, 1449)(385, 996, 1298)(387, 1195, 1396)(388, 1143, 
        1092)(389, 754, 792)(390, 1199, 1340)(392, 500, 455)(394, 785, 
        1050)(397, 572, 499)(399, 963, 1367)(400, 935, 897)(402, 1216, 
        1279)(404, 1220, 1178)(406, 1221, 561)(410, 696, 709)(412, 799, 
        1335)(415, 613, 1313)(418, 1073, 1077)(420, 1152, 1374)(421, 548, 
        1148)(423, 1232, 1387)(426, 473, 441)(427, 1235, 802)(428, 773, 
        1095)(429, 886, 740)(430, 667, 1391)(431, 859, 1453)(434, 806, 
        507)(435, 1242, 1075)(438, 1245, 833)(439, 910, 766)(442, 628, 
        1264)(445, 1174, 770)(447, 713, 610)(448, 725, 1309)(449, 1106, 
        1065)(453, 1036, 1267)(456, 604, 1346)(459, 486, 798)(460, 1194, 
        858)(462, 487, 511)(463, 481, 994)(464, 869, 533)(465, 685, 656)(466, 
        1258, 1332)(468, 1249, 1328)(469, 1187, 651)(471, 1070, 1448)(476, 652,
        707)(477, 883, 987)(478, 875, 864)(480, 1193, 1093)(483, 927, 892)(484,
        1273, 1196)(485, 1140, 1402)(488, 844, 1006)(490, 877, 1068)(493, 1034,
        940)(496, 1290, 912)(501, 868, 1240)(504, 1119, 1021)(505, 862, 
        1400)(508, 1212, 1438)(509, 1260, 938)(512, 723, 1069)(514, 1102, 
        1111)(516, 543, 1032)(519, 545, 777)(520, 1041, 617)(521, 1229, 
        1052)(524, 1296, 1265)(525, 716, 540)(527, 1318, 1377)(528, 772, 
        874)(529, 961, 1180)(536, 1325, 1461)(537, 1125, 1442)(538, 674, 
        922)(541, 1331, 690)(542, 783, 916)(544, 1333, 948)(546, 1302, 
        1141)(547, 1003, 1163)(551, 808, 776)(556, 1246, 1158)(558, 1280, 
        1162)(559, 1306, 1386)(562, 695, 1415)(563, 973, 983)(564, 1344, 
        1317)(571, 1301, 1336)(573, 666, 1087)(575, 768, 741)(576, 980, 
        765)(577, 1208, 1308)(580, 1057, 720)(581, 1257, 821)(587, 995, 
        941)(594, 597, 974)(601, 1243, 853)(602, 616, 759)(603, 746, 1345)(606,
        1361, 664)(608, 872, 1272)(611, 1356, 1355)(612, 1161, 779)(618, 879, 
        1200)(619, 743, 1103)(621, 1394, 1122)(622, 1253, 1456)(625, 1197, 
        805)(626, 880, 1215)(627, 1017, 932)(629, 1398, 641)(630, 1137, 
        1423)(635, 1401, 1440)(640, 906, 646)(642, 1233, 1186)(645, 993, 
        1171)(647, 1412, 1441)(654, 1413, 1079)(655, 1169, 1286)(661, 1375, 
        1159)(668, 1320, 815)(670, 1274, 1219)(671, 1217, 827)(672, 919, 
        1329)(675, 1362, 1436)(678, 1263, 1191)(691, 1157, 999)(698, 796, 
        931)(700, 1406, 1358)(701, 1237, 1428)(704, 1357, 1379)(705, 1300, 
        1225)(708, 1054, 847)(714, 1127, 1045)(717, 1039, 934)(719, 1389, 
        828)(724, 1023, 1011)(730, 1353, 914)(733, 1256, 1404)(735, 1414, 
        1250)(736, 1350, 1283)(737, 781, 891)(738, 1183, 1408)(742, 1281, 
        1422)(744, 1291, 1410)(745, 1170, 1409)(748, 1184, 851)(749, 1255, 
        841)(750, 1434, 1342)(751, 1179, 1138)(752, 814, 1010)(755, 1373, 
        1244)(757, 829, 982)(760, 1437, 1397)(761, 1439, 1112)(764, 1360, 
        1421)(767, 1247, 1405)(769, 1321, 1371)(782, 926, 944)(787, 1292, 
        885)(790, 945, 1430)(791, 1149, 1022)(793, 1444, 849)(795, 1027, 
        1009)(812, 819, 1254)(822, 1226, 863)(823, 1451, 1082)(825, 923, 
        1384)(831, 992, 1147)(835, 1452, 1210)(836, 957, 1420)(839, 1230, 
        1460)(842, 1129, 952)(848, 978, 956)(852, 1066, 1128)(854, 1363, 
        1277)(866, 1177, 1385)(881, 1288, 1433)(882, 1099, 950)(887, 1275, 
        1431)(894, 1334, 1211)(901, 1089, 1084)(913, 1028, 1166)(917, 1369, 
        1035)(918, 1352, 1181)(930, 1314, 1390)(939, 1293, 1205)(958, 1108, 
        1303)(959, 1261, 1459)(967, 1378, 1364)(971, 1136, 1399)(975, 1055, 
        1278)(976, 1319, 1443)(977, 1445, 997)(981, 991, 1262)(989, 1058, 
        1380)(1002, 1454, 1322)(1005, 1376, 1074)(1012, 1207, 1457)(1019, 1151,
        1312)(1030, 1096, 1043)(1048, 1110, 1101)(1056, 1080, 1276)(1060, 1209,
        1407)(1072, 1121, 1462)(1086, 1091, 1323)(1088, 1176, 1419)(1090, 1228,
        1388)(1104, 1424, 1202)(1113, 1120, 1172)(1115, 1287, 1417)(1123, 1359,
        1393)(1175, 1383, 1450)(1182, 1289, 1455)(1198, 1266, 1206)(1222, 1223,
        1299)(1224, 1341, 1435)(1239, 1343, 1284)(1241, 1327, 1330)(1252, 1403,
        1427)(1259, 1305, 1270)(1295, 1382, 1432)(1297, 1351, 1463)(1304, 1426,
        1315)(1311, 1347, 1372)(1354, 1418, 1381)

orbs[18];
GSet{@ 14, 516, 1309, 506, 826, 1171, 953, 565, 1111, 91, 1107, 1295, 427, 282,
95, 1287, 435, 851, 1168, 511, 428, 1294, 50, 429, 508, 527, 665, 463, 563, 
1459, 1220, 478, 90, 1277, 15, 1108, 1389, 1000, 569, 1296, 636, 564, 464, 441,
501, 1366, 1085, 1407, 1135, 321, 1001, 472, 1048, 1103, 505, 319, 101, 85, 
280, 525, 1110, 1378, 1434, 442, 1408, 952, 438, 241, 84, 89, 493, 1317, 81, 
473, 468, 443, 1243, 103, 462, 320, 1223, 1308, 785, 518, 477, 514, 157, 492, 
434, 1236, 465, 83, 372, 393, 507, 786, 1237, 838, 751, 1039, 1346, 1165, 439, 
491, 281, 873, 1268, 57, 119, 1036, 1288, 1422, 1013, 1267, 640, 954, 1104, 
102, 108, 92 @}
> orbs[21];
GSet{@ 64, 1200, 763, 610, 1311, 1095, 663, 722, 1081, 1114, 1038, 760, 1255, 
735, 1151, 990, 166, 410, 560, 1029, 1195, 586, 489, 800, 672, 680, 573, 732, 
1174, 448, 799, 907, 394, 1461, 1435, 1014, 561, 661, 146, 1180, 1394, 1424, 
731, 707, 965, 1460, 1379, 1265, 1119, 659, 1176, 1370, 1041, 1310, 998, 519, 
1093, 158, 133, 1454, 1415, 447, 1404, 148, 86, 1202, 616, 449, 249, 1008, 
1433, 652, 457, 676, 323, 638, 733, 367, 868, 1452, 1266, 1341, 977, 1438, 
1432, 1028, 752, 1356, 1009, 277, 1388, 355, 312, 470, 590, 766, 1453, 639, 
292, 630, 1250, 373, 285, 1290, 1285, 1096, 1247, 1098, 702, 1264, 1456, 872, 
1363, 1175, 474, 662, 1312, 828, 1208, 1061 @}
\end{verbatim}}
\subsection{$J_1$ of degree 1540: $[1540,20,640]_2$}
{\small
\begin{verbatim}
> Generators(a2); 
{
    (1, 3, 6)(2, 4, 8)(5, 9, 14)(7, 11, 17)(10, 15, 22)(12, 18, 26)(13, 19, 
        28)(16, 23, 33)(20, 29, 39)(21, 30, 40)(24, 34, 45)(25, 35, 47)(27, 37,
        50)(31, 41, 55)(32, 42, 56)(36, 48, 49)(38, 51, 63)(43, 57, 68)(44, 58,
        46)(53, 64, 76)(54, 65, 78)(59, 70, 84)(60, 71, 86)(61, 72, 88)(62, 73,
        90)(66, 79, 96)(67, 80, 98)(69, 82, 101)(74, 91, 75)(77, 93, 113)(81, 
        99, 100)(83, 102, 122)(85, 104, 125)(87, 106, 128)(89, 108, 131)(92, 
        111, 112)(94, 114, 136)(95, 115, 138)(97, 117, 141)(103, 123, 124)(105,
        126, 150)(107, 129, 130)(109, 132, 155)(110, 133, 157)(116, 139, 
        140)(118, 142, 165)(119, 143, 167)(120, 144, 169)(121, 145, 170)(127, 
        151, 175)(134, 158, 183)(135, 159, 185)(137, 160, 186)(146, 171, 
        197)(147, 172, 199)(148, 173, 200)(149, 174, 201)(152, 176, 204)(153, 
        177, 206)(154, 178, 208)(156, 180, 211)(161, 187, 219)(162, 188, 
        221)(163, 189, 223)(164, 190, 225)(166, 192, 228)(168, 194, 230)(179, 
        209, 210)(181, 212, 248)(182, 213, 249)(184, 215, 252)(191, 226, 
        227)(193, 229, 265)(195, 231, 267)(196, 232, 269)(198, 234, 272)(202, 
        238, 276)(203, 239, 278)(205, 241, 281)(207, 243, 284)(214, 250, 
        290)(216, 253, 217)(218, 254, 295)(220, 256, 298)(222, 258, 301)(224, 
        260, 304)(233, 270, 271)(235, 273, 315)(237, 274, 316)(240, 279, 
        280)(242, 282, 324)(244, 285, 245)(246, 286, 329)(247, 287, 331)(251, 
        291, 334)(255, 296, 297)(257, 299, 341)(259, 302, 303)(261, 305, 
        347)(262, 306, 348)(263, 307, 350)(264, 308, 352)(266, 309, 353)(268, 
        311, 356)(275, 317, 362)(277, 319, 365)(283, 325, 370)(288, 332, 
        378)(289, 333, 380)(292, 335, 383)(293, 336, 385)(294, 337, 386)(300, 
        342, 390)(310, 354, 355)(312, 357, 404)(313, 358, 406)(314, 359, 
        408)(318, 363, 364)(320, 366, 414)(321, 367, 416)(322, 368, 418)(323, 
        369, 420)(326, 371, 423)(327, 372, 425)(328, 373, 427)(330, 375, 
        430)(338, 387, 442)(339, 388, 444)(340, 389, 446)(343, 391, 449)(344, 
        392, 451)(345, 393, 453)(346, 394, 455)(349, 397, 458)(351, 399, 
        461)(360, 409, 361)(374, 428, 429)(376, 431, 491)(377, 432, 493)(379, 
        434, 496)(381, 436, 499)(382, 437, 501)(384, 439, 504)(395, 456, 
        396)(398, 459, 460)(400, 462, 521)(401, 463, 523)(402, 464, 525)(403, 
        465, 527)(405, 467, 530)(407, 469, 533)(410, 471, 536)(411, 472, 
        538)(412, 473, 540)(413, 474, 542)(415, 476, 545)(417, 478, 547)(419, 
        480, 550)(421, 482, 553)(422, 483, 555)(424, 485, 558)(426, 486, 
        559)(433, 494, 495)(435, 497, 569)(438, 502, 503)(440, 505, 577)(441, 
        506, 579)(443, 508, 582)(445, 510, 585)(447, 470, 534)(448, 511, 
        587)(450, 454, 515)(452, 513, 590)(457, 516, 593)(466, 528, 529)(468, 
        531, 608)(475, 543, 544)(477, 490, 563)(479, 548, 549)(481, 551, 
        627)(484, 556, 557)(487, 560, 636)(488, 561, 638)(489, 562, 640)(492, 
        564, 641)(498, 570, 648)(500, 572, 651)(507, 580, 581)(509, 583, 
        661)(512, 588, 667)(514, 591, 592)(517, 594, 673)(518, 595, 675)(519, 
        596, 677)(520, 597, 679)(522, 599, 682)(524, 601, 685)(526, 603, 
        688)(532, 609, 692)(535, 612, 696)(537, 614, 699)(539, 616, 702)(541, 
        618, 705)(546, 622, 708)(552, 628, 715)(554, 630, 718)(565, 642, 
        731)(566, 643, 733)(567, 644, 735)(568, 645, 619)(571, 649, 650)(573, 
        652, 742)(574, 653, 744)(575, 654, 746)(576, 655, 748)(578, 657, 
        751)(584, 662, 755)(586, 664, 758)(589, 668, 761)(598, 680, 681)(600, 
        683, 774)(602, 686, 687)(604, 635, 723)(605, 689, 780)(606, 690, 
        782)(607, 691, 784)(610, 693, 787)(611, 694, 757)(613, 697, 698)(615, 
        700, 793)(617, 703, 704)(620, 706, 798)(621, 707, 800)(623, 709, 
        803)(624, 710, 805)(625, 711, 807)(626, 712, 809)(629, 716, 717)(631, 
        719, 814)(632, 720, 816)(633, 721, 818)(634, 722, 820)(637, 725, 
        824)(639, 727, 827)(646, 737, 647)(656, 749, 750)(658, 752, 850)(659, 
        753, 852)(660, 754, 854)(663, 756, 695)(665, 759, 671)(666, 760, 
        860)(669, 762, 863)(670, 763, 865)(672, 764, 867)(674, 766, 870)(676, 
        768, 734)(678, 769, 833)(684, 775, 877)(701, 794, 893)(713, 810, 
        714)(724, 822, 823)(726, 825, 919)(728, 828, 801)(729, 829, 923)(730, 
        830, 925)(732, 832, 928)(736, 835, 897)(738, 837, 933)(739, 838, 
        935)(740, 839, 937)(741, 840, 939)(743, 842, 942)(745, 844, 945)(747, 
        845, 946)(765, 868, 869)(767, 871, 969)(770, 873, 971)(771, 874, 
        973)(772, 875, 811)(773, 876, 975)(776, 878, 778)(779, 879, 979)(781, 
        881, 982)(783, 883, 985)(785, 885, 988)(786, 886, 990)(788, 888, 
        993)(789, 889, 995)(790, 890, 997)(791, 891, 999)(792, 892, 1001)(795, 
        894, 1004)(796, 895, 1006)(797, 896, 1007)(799, 898, 1008)(802, 899, 
        1010)(804, 901, 1013)(806, 903, 1015)(808, 905, 1018)(812, 906, 
        1020)(813, 907, 1021)(815, 909, 1023)(817, 911, 1026)(819, 913, 
        1029)(821, 915, 978)(826, 920, 1034)(831, 926, 927)(834, 929, 930)(836,
        931, 1040)(841, 940, 941)(843, 943, 1049)(846, 947, 1052)(847, 948, 
        1054)(848, 949, 849)(851, 951, 1058)(853, 953, 1061)(855, 955, 
        1063)(856, 956, 1065)(857, 957, 1067)(858, 958, 1069)(859, 959, 
        1070)(861, 961, 1073)(862, 962, 1075)(864, 964, 1078)(866, 965, 
        1079)(872, 970, 1083)(880, 980, 1091)(882, 983, 984)(884, 986, 
        1096)(887, 991, 992)(900, 1011, 1012)(902, 996, 1105)(904, 1016, 
        1017)(908, 924, 1022)(910, 1024, 1126)(912, 1027, 1028)(914, 1030, 
        1031)(916, 977, 1089)(917, 1032, 1133)(918, 1033, 1135)(921, 1035, 
        1138)(922, 1036, 1140)(932, 1041, 1146)(934, 1043, 1149)(936, 1045, 
        1152)(938, 1047, 1155)(944, 1050, 1157)(950, 1056, 1160)(952, 1059, 
        1060)(954, 1062, 1165)(960, 1071, 1173)(963, 1076, 1077)(966, 1080, 
        1180)(967, 1081, 1182)(968, 1082, 1184)(972, 1085, 1188)(974, 1086, 
        1189)(976, 1088, 1191)(981, 1092, 1194)(987, 1097, 1200)(989, 1099, 
        1203)(994, 1103, 1208)(998, 1107, 1211)(1000, 1109, 1214)(1002, 1111, 
        1217)(1003, 1112, 1219)(1005, 1114, 1222)(1009, 1116, 1224)(1014, 1120,
        1104)(1019, 1124, 1055)(1025, 1127, 1227)(1037, 1141, 1238)(1038, 1142,
        1240)(1039, 1143, 1166)(1042, 1147, 1148)(1044, 1150, 1246)(1046, 1153,
        1154)(1048, 1156, 1250)(1053, 1159, 1237)(1057, 1161, 1254)(1064, 1167,
        1074)(1066, 1168, 1259)(1068, 1170, 1260)(1072, 1174, 1207)(1084, 1186,
        1187)(1087, 1178, 1268)(1090, 1193, 1278)(1093, 1195, 1281)(1094, 1196,
        1119)(1095, 1197, 1284)(1098, 1201, 1202)(1100, 1204, 1289)(1101, 1205,
        1291)(1102, 1206, 1292)(1106, 1209, 1295)(1108, 1212, 1213)(1110, 1215,
        1299)(1113, 1220, 1221)(1115, 1223, 1125)(1117, 1225, 1306)(1118, 1226,
        1283)(1121, 1179, 1123)(1128, 1228, 1310)(1129, 1229, 1312)(1130, 1230,
        1314)(1131, 1181, 1270)(1132, 1231, 1192)(1134, 1190, 1276)(1136, 1233,
        1169)(1137, 1234, 1317)(1139, 1236, 1320)(1144, 1241, 1324)(1145, 1242,
        1325)(1151, 1247, 1328)(1158, 1252, 1253)(1162, 1255, 1334)(1163, 1256,
        1335)(1164, 1257, 1337)(1171, 1261, 1340)(1172, 1262, 1243)(1175, 1265,
        1287)(1176, 1266, 1343)(1177, 1267, 1345)(1183, 1272, 1350)(1185, 1274,
        1303)(1198, 1285, 1199)(1210, 1296, 1364)(1216, 1300, 1369)(1232, 1316,
        1382)(1235, 1318, 1319)(1239, 1322, 1388)(1244, 1326, 1391)(1245, 1327,
        1392)(1248, 1329, 1394)(1249, 1275, 1353)(1251, 1331, 1396)(1258, 1338,
        1400)(1263, 1342, 1264)(1269, 1293, 1363)(1271, 1348, 1349)(1273, 1351,
        1412)(1277, 1355, 1416)(1279, 1356, 1417)(1282, 1358, 1294)(1286, 1361,
        1421)(1288, 1362, 1290)(1297, 1365, 1423)(1298, 1366, 1425)(1301, 1370,
        1429)(1302, 1371, 1431)(1304, 1311, 1378)(1305, 1372, 1433)(1307, 1374,
        1436)(1308, 1375, 1437)(1309, 1376, 1439)(1313, 1380, 1444)(1321, 1386,
        1387)(1323, 1330, 1395)(1332, 1397, 1454)(1333, 1393, 1422)(1336, 1399,
        1414)(1339, 1401, 1458)(1341, 1403, 1460)(1344, 1406, 1463)(1346, 1408,
        1354)(1347, 1409, 1415)(1352, 1413, 1453)(1357, 1418, 1419)(1359, 1420,
        1360)(1367, 1426, 1368)(1373, 1434, 1435)(1377, 1440, 1441)(1379, 1442,
        1478)(1381, 1445, 1482)(1383, 1446, 1484)(1384, 1447, 1486)(1385, 1448,
        1477)(1389, 1450, 1488)(1390, 1451, 1489)(1398, 1455, 1456)(1402, 1407,
        1459)(1404, 1461, 1466)(1405, 1462, 1468)(1410, 1428, 1427)(1411, 1465,
        1449)(1424, 1470, 1483)(1430, 1473, 1438)(1432, 1474, 1499)(1443, 1479,
        1502)(1452, 1490, 1509)(1457, 1492, 1471)(1464, 1493, 1510)(1467, 1495,
        1513)(1469, 1496, 1497)(1472, 1480, 1503)(1475, 1500, 1518)(1476, 1501,
        1520)(1481, 1504, 1521)(1485, 1506, 1524)(1487, 1507, 1491)(1494, 1511,
        1526)(1498, 1515, 1517)(1505, 1522, 1523)(1508, 1525, 1530)(1512, 1527,
        1531)(1514, 1528, 1532)(1519, 1529, 1533)(1534, 1537, 1540)(1535, 1538,
        1536),
    (1, 2)(3, 5)(4, 7)(6, 10)(8, 12)(9, 13)(11, 16)(14, 20)(15, 21)(17, 24)(18,
        25)(19, 27)(22, 31)(23, 32)(26, 36)(28, 38)(29, 30)(33, 43)(34, 44)(35,
        46)(37, 49)(39, 52)(40, 53)(41, 54)(42, 55)(47, 59)(48, 60)(50, 61)(51,
        62)(56, 66)(57, 67)(58, 69)(63, 74)(64, 75)(65, 77)(68, 81)(70, 83)(71,
        85)(72, 87)(73, 89)(76, 92)(78, 94)(79, 95)(80, 97)(82, 100)(84, 
        103)(86, 105)(88, 107)(90, 109)(91, 110)(93, 112)(96, 116)(98, 118)(99,
        119)(101, 120)(102, 121)(104, 124)(106, 127)(108, 130)(111, 134)(113, 
        135)(115, 137)(117, 140)(122, 146)(123, 147)(125, 148)(126, 149)(128, 
        152)(129, 153)(131, 154)(133, 156)(136, 160)(138, 161)(139, 162)(141, 
        163)(142, 164)(143, 166)(144, 168)(145, 169)(150, 151)(155, 179)(157, 
        181)(158, 182)(159, 184)(165, 191)(167, 193)(170, 195)(171, 196)(172, 
        198)(173, 174)(175, 202)(176, 203)(177, 205)(178, 207)(180, 210)(183, 
        214)(185, 216)(186, 217)(187, 218)(188, 220)(189, 222)(190, 224)(192, 
        227)(197, 233)(199, 235)(200, 236)(201, 237)(204, 240)(206, 242)(208, 
        244)(209, 245)(211, 246)(212, 247)(213, 248)(215, 251)(219, 255)(221, 
        257)(223, 259)(225, 261)(226, 262)(228, 263)(229, 264)(230, 265)(231, 
        266)(232, 268)(234, 271)(238, 275)(239, 277)(241, 280)(243, 283)(249, 
        288)(250, 289)(252, 292)(253, 293)(254, 294)(256, 297)(258, 300)(260, 
        303)(267, 310)(269, 312)(270, 313)(272, 314)(273, 299)(274, 315)(276, 
        318)(278, 320)(279, 321)(281, 322)(282, 323)(284, 326)(285, 327)(286, 
        328)(287, 330)(290, 291)(295, 338)(296, 339)(298, 340)(301, 343)(302, 
        344)(304, 345)(305, 346)(307, 349)(308, 351)(309, 352)(311, 355)(316, 
        360)(317, 361)(319, 364)(324, 325)(329, 374)(331, 376)(332, 377)(333, 
        379)(334, 381)(335, 382)(336, 384)(337, 385)(341, 342)(347, 395)(348, 
        396)(350, 398)(353, 400)(354, 401)(356, 402)(357, 403)(358, 405)(359, 
        407)(362, 410)(363, 411)(365, 412)(366, 413)(367, 415)(368, 417)(369, 
        419)(370, 421)(371, 422)(372, 424)(373, 426)(375, 429)(378, 433)(380, 
        435)(383, 438)(386, 440)(387, 441)(388, 443)(389, 445)(390, 447)(391, 
        448)(392, 450)(393, 452)(394, 454)(397, 457)(399, 460)(404, 466)(406, 
        468)(408, 470)(409, 446)(414, 475)(416, 477)(418, 479)(420, 481)(423, 
        484)(425, 486)(427, 487)(428, 488)(430, 489)(431, 490)(432, 492)(434, 
        495)(436, 498)(437, 500)(439, 503)(442, 507)(444, 509)(449, 455)(451, 
        512)(453, 514)(456, 516)(458, 517)(459, 518)(461, 519)(462, 520)(463, 
        522)(464, 524)(465, 526)(467, 529)(469, 532)(471, 535)(472, 537)(473, 
        539)(474, 541)(476, 544)(478, 546)(480, 549)(482, 552)(483, 554)(485, 
        557)(491, 564)(493, 565)(494, 566)(496, 567)(497, 568)(499, 571)(501, 
        573)(502, 574)(504, 575)(505, 576)(506, 578)(508, 581)(510, 584)(511, 
        586)(513, 589)(515, 592)(521, 598)(523, 600)(525, 602)(527, 604)(528, 
        605)(530, 606)(531, 607)(533, 610)(534, 611)(536, 613)(538, 615)(540, 
        617)(542, 619)(543, 620)(545, 621)(547, 623)(548, 624)(550, 625)(551, 
        626)(553, 629)(555, 631)(556, 632)(558, 633)(559, 634)(560, 635)(561, 
        637)(562, 639)(563, 622)(569, 646)(570, 647)(572, 650)(577, 656)(580, 
        658)(582, 659)(583, 660)(585, 663)(587, 665)(588, 666)(590, 669)(591, 
        670)(593, 671)(594, 672)(595, 674)(596, 676)(597, 678)(599, 681)(601, 
        684)(603, 687)(608, 609)(612, 695)(614, 698)(616, 701)(618, 704)(627, 
        713)(628, 714)(630, 717)(636, 724)(638, 726)(640, 728)(641, 729)(642, 
        730)(643, 732)(644, 734)(645, 736)(648, 738)(649, 739)(651, 740)(652, 
        741)(653, 743)(654, 745)(655, 747)(657, 750)(661, 662)(664, 757)(667, 
        668)(673, 765)(675, 767)(677, 769)(679, 770)(680, 771)(682, 772)(683, 
        773)(685, 776)(686, 777)(688, 778)(689, 779)(690, 781)(691, 783)(692, 
        785)(693, 786)(694, 788)(696, 789)(697, 790)(699, 791)(700, 792)(702, 
        795)(703, 796)(705, 797)(707, 799)(708, 801)(709, 802)(710, 804)(711, 
        806)(712, 808)(715, 811)(716, 812)(719, 813)(720, 815)(721, 817)(722, 
        819)(723, 821)(725, 823)(727, 826)(731, 831)(733, 833)(735, 834)(737, 
        836)(742, 841)(744, 843)(746, 845)(748, 846)(749, 847)(751, 848)(752, 
        849)(753, 851)(754, 853)(755, 855)(756, 856)(758, 857)(759, 858)(760, 
        859)(761, 861)(762, 862)(763, 864)(764, 866)(766, 869)(768, 872)(774, 
        775)(780, 880)(782, 882)(784, 884)(787, 887)(793, 794)(798, 897)(800, 
        829)(803, 900)(805, 902)(807, 904)(809, 867)(810, 876)(814, 908)(816, 
        910)(818, 912)(820, 914)(822, 916)(824, 917)(825, 918)(827, 921)(828, 
        922)(830, 924)(832, 927)(835, 930)(837, 932)(838, 934)(839, 936)(840, 
        938)(842, 941)(844, 944)(850, 950)(852, 952)(854, 954)(860, 960)(863, 
        963)(865, 959)(868, 966)(870, 967)(871, 968)(873, 955)(874, 972)(875, 
        974)(877, 976)(878, 977)(879, 978)(881, 981)(883, 984)(885, 987)(886, 
        989)(888, 992)(889, 994)(890, 996)(891, 998)(892, 1000)(893, 1002)(894,
        1003)(895, 1005)(896, 942)(898, 929)(899, 1009)(901, 1012)(903, 
        1014)(905, 1017)(906, 1019)(907, 1020)(909, 1022)(911, 1025)(913, 
        1028)(915, 1031)(919, 920)(923, 1023)(925, 1037)(926, 1038)(928, 
        1039)(931, 1007)(933, 1042)(935, 1044)(937, 1046)(939, 973)(940, 
        1048)(943, 1006)(945, 947)(946, 1051)(948, 1053)(949, 1055)(951, 
        1057)(953, 1060)(956, 1064)(957, 1066)(958, 1068)(961, 1072)(962, 
        1074)(964, 1077)(965, 1069)(969, 970)(971, 1084)(975, 1087)(979, 
        1090)(980, 1059)(982, 1093)(983, 1094)(985, 1095)(988, 1098)(990, 
        1100)(991, 1101)(993, 1102)(995, 1104)(997, 1106)(999, 1108)(1001, 
        1110)(1004, 1113)(1008, 1115)(1010, 1117)(1011, 1118)(1013, 1119)(1015,
        1121)(1016, 1122)(1018, 1123)(1021, 1054)(1024, 1125)(1026, 1128)(1027,
        1129)(1029, 1130)(1030, 1131)(1032, 1132)(1033, 1134)(1034, 1136)(1035,
        1137)(1036, 1139)(1040, 1144)(1041, 1145)(1043, 1148)(1045, 1151)(1047,
        1154)(1049, 1050)(1052, 1158)(1056, 1153)(1058, 1162)(1061, 1163)(1062,
        1164)(1063, 1166)(1065, 1073)(1067, 1169)(1070, 1171)(1071, 1172)(1075,
        1175)(1076, 1176)(1078, 1177)(1079, 1178)(1080, 1179)(1081, 1181)(1082,
        1183)(1083, 1185)(1085, 1187)(1086, 1155)(1088, 1190)(1089, 1192)(1091,
        1092)(1096, 1198)(1097, 1199)(1099, 1202)(1103, 1207)(1105, 1120)(1107,
        1210)(1109, 1213)(1111, 1216)(1112, 1218)(1114, 1221)(1116, 1140)(1124,
        1189)(1126, 1127)(1133, 1191)(1135, 1232)(1138, 1235)(1141, 1237)(1142,
        1239)(1143, 1167)(1146, 1243)(1147, 1244)(1150, 1245)(1152, 1248)(1156,
        1249)(1157, 1251)(1159, 1253)(1160, 1161)(1165, 1186)(1168, 1258)(1170,
        1233)(1173, 1263)(1174, 1264)(1180, 1269)(1182, 1271)(1184, 1273)(1188,
        1275)(1193, 1277)(1194, 1279)(1195, 1280)(1196, 1282)(1197, 1283)(1200,
        1286)(1201, 1266)(1203, 1287)(1204, 1288)(1205, 1290)(1206, 1214)(1208,
        1293)(1209, 1294)(1211, 1297)(1212, 1298)(1215, 1291)(1217, 1219)(1220,
        1301)(1222, 1302)(1223, 1303)(1224, 1304)(1225, 1305)(1226, 1307)(1227,
        1308)(1228, 1309)(1229, 1311)(1230, 1313)(1231, 1315)(1234, 1259)(1236,
        1319)(1238, 1321)(1240, 1265)(1241, 1323)(1242, 1324)(1246, 1247)(1250,
        1330)(1252, 1332)(1254, 1329)(1255, 1333)(1256, 1278)(1257, 1336)(1260,
        1339)(1262, 1341)(1267, 1344)(1268, 1346)(1270, 1347)(1272, 1349)(1274,
        1352)(1276, 1354)(1281, 1357)(1284, 1359)(1285, 1360)(1292, 1338)(1295,
        1296)(1299, 1367)(1300, 1368)(1306, 1373)(1310, 1377)(1312, 1379)(1314,
        1348)(1316, 1381)(1317, 1383)(1318, 1384)(1320, 1385)(1322, 1387)(1325,
        1389)(1326, 1390)(1327, 1391)(1328, 1393)(1331, 1375)(1334, 1356)(1335,
        1398)(1340, 1402)(1342, 1404)(1343, 1405)(1345, 1407)(1350, 1410)(1351,
        1411)(1353, 1414)(1355, 1415)(1358, 1419)(1361, 1406)(1362, 1388)(1363,
        1409)(1364, 1422)(1365, 1392)(1366, 1424)(1369, 1427)(1370, 1428)(1371,
        1430)(1372, 1432)(1374, 1435)(1376, 1438)(1378, 1441)(1380, 1443)(1382,
        1401)(1386, 1449)(1395, 1452)(1396, 1453)(1397, 1413)(1399, 1456)(1400,
        1457)(1403, 1459)(1408, 1464)(1412, 1454)(1416, 1466)(1417, 1418)(1420,
        1467)(1421, 1468)(1423, 1469)(1425, 1471)(1426, 1465)(1429, 1472)(1431,
        1437)(1433, 1439)(1434, 1475)(1436, 1476)(1440, 1474)(1442, 1477)(1444,
        1480)(1445, 1481)(1446, 1483)(1447, 1485)(1450, 1487)(1451, 1460)(1455,
        1491)(1458, 1493)(1461, 1488)(1463, 1494)(1470, 1497)(1473, 1498)(1478,
        1479)(1484, 1505)(1486, 1502)(1489, 1508)(1490, 1507)(1495, 1512)(1496,
        1514)(1499, 1516)(1500, 1517)(1501, 1519)(1503, 1515)(1504, 1510)(1506,
        1523)(1511, 1513)(1518, 1524)(1520, 1527)(1522, 1529)(1525, 1526)(1528,
        1530)(1531, 1534)(1532, 1535)(1533, 1536)(1537, 1539)(1538, 1540)
}
orbs[7];
GSet{@ 11, 220, 592, 1043, 580, 770, 1324, 167, 859, 690, 1090, 895, 1199, 
1262, 833, 340, 490, 437, 1098, 1059, 1497, 57, 1013, 528, 1382, 999, 523, 435,
122, 304, 856, 1172, 585, 319, 533, 324, 997, 1180, 371, 66, 194, 79, 1462, 
665, 1029, 574, 1094, 1390, 59, 988, 1170, 1490, 1174, 156, 714, 600, 889 @}
> orbs[13];
GSet{@ 3, 1367, 51, 1291, 1016, 1355, 1315, 681, 952, 568, 438, 1131, 1348, 
832, 4, 90, 1330, 1453, 400, 697, 506, 754, 1381, 802, 1334, 1275, 1322, 186, 
813, 1116, 1352, 29, 1303, 740, 384, 1085, 706, 178, 98, 1409, 78, 1135, 612, 
1107, 1081, 1253, 885, 1268, 75, 1285, 86, 1192, 661, 1519, 367, 1203, 1044, 
297, 775, 283, 1399, 465, 474, 1056, 1527, 1244, 373, 858, 1371, 263, 749, 977,
1338, 1358, 1425, 757, 1224, 800, 1128, 175, 285, 909, 246, 34, 990, 905, 1308,
351, 292, 509, 702, 358, 805, 637, 949, 890, 747, 918, 633, 170, 233, 1383, 
981, 603, 87, 1046, 1305, 750, 419, 1474, 1154, 541, 836, 970 @}

\end{verbatim}}
\subsection{$J_2$ of degree 100: $[100,36,16]_2$}
{\small \begin{verbatim}
 Generators(a2); 
    (1, 2, 4, 6, 3)(5, 7, 10, 14, 21)(8, 11, 16, 17, 23)(9, 12, 18, 25, 32)(13,
        19, 26, 34, 44)(15, 22, 20, 27, 35)(24, 30, 39, 51, 65)(28, 36, 47, 60,
        48)(29, 37, 49, 62, 74)(31, 40, 53, 43, 55)(33, 42, 41, 54, 67)(38, 45,
        57, 56, 69)(46, 58, 71, 82, 89)(50, 63, 75, 73, 83)(52, 66, 78, 86, 
        59)(61, 72, 77, 85, 93)(64, 76, 79, 87, 95)(68, 80, 84, 91, 94)(70, 81,
        88, 97, 96)(90, 98, 92, 99, 100),
    (2, 3)(4, 5)(6, 8)(7, 9)(10, 13)(11, 15)(12, 17)(14, 20)(18, 24)(21, 
        28)(22, 29)(25, 31)(26, 33)(30, 38)(32, 41)(34, 43)(35, 45)(36, 46)(37,
        48)(39, 50)(40, 52)(44, 56)(47, 59)(49, 61)(51, 64)(53, 63)(55, 68)(58,
        70)(62, 73)(65, 77)(67, 79)(72, 78)(74, 81)(75, 82)(76, 84)(83, 90)(85,
        92)(87, 94)(88, 96)(91, 99)
\\orbit taken for blocks of design orbs[2] 1-(100, 36, 36)
GSet{@ 2, 3, 7, 25, 31, 54, 87, 9, 19, 85, 77, 66, 60, 42, 71, 23, 88,
94, 64, 73, 92, 93, 61, 96, 65, 99, 49, 97, 91, 51, 86, 98, 62, 90,
95, 83 @}
\\orbit taken for blocks of design orbs[3] 1-(100, 63, 63)
orbs[3];
GSet{@ 4, 5, 11, 70, 21, 26, 12, 63, 72, 46, 22, 47, 15, 17, 29, 68,
36, 6, 53, 58, 40, 50, 78, 76, 28, 18, 33, 55, 10, 82, 30, 79, 32, 67,
89, 41, 57, 81, 24, 14, 56, 44, 38, 69, 59, 48, 100, 75, 37, 20, 45,
8, 16, 84, 80, 74, 52, 13, 43, 39, 35, 34, 27 @}
\end{verbatim}}
\subsection{$J_2$ of degree 280: $[280,13,128]_2$}
{\small \begin{verbatim}
Generators(a2);

{ (1, 2)(3, 5)(6, 9)(7, 11)(8, 13)(12, 18)(15, 22)(16, 24)(17, 25)(19,
    28)(20, 29)(21, 31)(23, 34)(27, 38)(30, 42)(32, 45)(33, 46)(35,
    36)(37, 50)(39, 53)(40, 55)(41, 57)(43, 60)(47, 65)(48, 67)(49,
    69)(51, 70)(52, 71)(54, 74)(56, 77)(59, 80)(61, 83)(62, 84)(63,
    85)(64, 87)(66, 89)(68, 92)(72, 95)(73, 97)(75, 99)(76, 100)(78,
    103)(79, 104)(81, 107)(82, 109)(86, 101)(88, 114)(90, 117)(91,
    118)(93, 121)(94, 123)(96, 125)(98, 128)(105, 134)(106, 135)(108,
    138)(110, 120)(111, 122)(112, 143)(113, 145)(115, 147)(116,
    149)(119, 141)(124, 155)(127, 158)(130, 161)(131, 163)(132,
    164)(133, 166)(137, 171)(139, 174)(140, 175)(142, 177)(144,
    179)(146, 182)(148, 154)(150, 184)(151, 186)(152, 173)(156,
    169)(157, 192)(160, 194)(162, 195)(165, 197)(167, 198)(168,
    199)(172, 181)(176, 204)(178, 206)(180, 209)(185, 213)(187,
    216)(188, 217)(190, 219)(191, 220)(196, 226)(201, 230)(202,
    232)(203, 234)(205, 235)(212, 240)(214, 243)(218, 246)(221,
    249)(222, 250)(223, 233)(224, 252)(225, 253)(227, 254)(236,
    259)(238, 242)(241, 248)(251, 257)(256, 275)(260, 276)(262,
    266)(264, 271)(268, 278)(269, 272)(273, 277),

    (1, 3, 6, 10, 16)(2, 4, 7, 12, 19)(5, 8, 14, 21, 32)(9, 15, 23,
        35, 24)(11, 17, 26, 37, 51)(13, 20, 30, 43, 61)(18, 27, 39,
        54, 75)(22, 33, 47, 66, 90)(25, 36, 49, 65, 50)(28, 40, 56,
        78, 57)(29, 41, 58, 79, 105)(31, 44, 62, 70, 94)(34, 48, 68,
        93, 122)(38, 52, 72, 96, 126)(42, 59, 81, 108, 139)(45, 63,
        86, 113, 87)(46, 64, 88, 115, 148)(53, 73, 98, 129, 74)(55,
        76, 101, 131, 121)(60, 82, 110, 141, 69)(67, 91, 119, 153,
        189)(71, 84, 83, 111, 142)(77, 102, 132, 165, 103)(80, 106,
        136, 170, 171)(85, 112, 144, 180, 210)(89, 116, 150, 185,
        214)(92, 120, 128, 160, 164)(95, 124, 156, 134, 168)(97, 127,
        159, 193, 223)(99, 109, 140, 176, 161)(100, 130, 162, 194,
        224)(104, 133, 167, 163, 196)(107, 137, 172, 201, 231)(114,
        146, 135, 169, 200)(117, 151, 187, 138, 173)(118, 152, 188,
        218, 149)(123, 154, 190, 204, 206)(125, 157, 175, 203,
        158)(143, 178, 207, 236, 260)(145, 181, 182, 211, 239)(147,
        183, 155, 191, 221)(166, 197, 227, 255, 274)(174, 202, 233,
        258, 234)(177, 205, 184, 212, 241)(179, 208, 237, 261,
        276)(186, 215, 244, 243, 265)(192, 222, 251, 271, 259)(195,
        225, 246, 266, 277)(198, 228, 254, 273, 235)(199, 229, 256,
        250, 270)(209, 238, 262, 275, 226)(213, 242, 264, 216,
        245)(217, 230, 252, 232, 257)(219, 247, 267, 249, 269)(220,
        248, 268, 279, 280)(240, 263, 253, 272, 278) } 
\\orbit taken for blocks of design > 
orbs[3]; 
GSet{@ 6, 275, 273, 197, 91, 226, 259, 163, 175, 100, 127, 155, 249,
        161, 77, 234, 193, 224, 76, 195, 121, 178, 43, 200, 61, 219,
        99, 107, 92, 235, 216, 85, 212, 139, 105, 88, 46, 201, 252,
        42, 136, 106, 229, 230, 117, 214, 34, 246, 123, 270, 274, 7,
        160, 18, 108, 114, 206, 260, 227, 204, 11, 64, 36, 255, 232,
        278, 208, 222, 172, 73, 165, 41, 38, 143, 75, 170, 72, 168,
        79, 158, 95, 209, 87, 81, 17, 262, 269, 157, 261, 37, 266,
        241, 40, 149, 54, 228, 51, 66, 49, 183, 69, 267, 98, 10, 220,
        14, 58, 31 @}
\end{verbatim}}

\subsection{$J_2$ of degree 315, dimension 28: $[315,28,64]_2$}
{\small \begin{verbatim} 
Generators(a2); 
{ (1, 3, 6, 11, 19)(2, 4, 8, 14, 23)(5, 9, 16, 26, 40)(7, 12, 20, 31,
 48)(10, 17, 28, 43, 65)(13, 21, 33, 51, 75)(15, 24, 37, 57, 84)(18,
 29, 45, 67, 93)(22, 34, 53, 78, 104)(25, 38, 59, 56, 82)(27, 41, 63,
 88, 117)(30, 46, 69, 39, 60)(32, 49, 73, 98, 131)(35, 54, 79, 106,
 80)(36, 55, 81, 108, 141)(42, 64, 90, 119, 156)(47, 70, 95, 103,
 137)(50, 74, 85, 111, 146)(52, 76, 101, 135, 58)(61, 86, 113, 149,
 114)(62, 87, 115, 151, 191)(66, 91, 120, 158, 198)(68, 94, 124, 162,
 201)(71, 96, 127, 166, 128)(72, 97, 129, 168, 207)(77, 102, 136, 174,
 215)(83, 110, 144, 184, 145)(89, 118, 139, 177, 186)(92, 121, 160,
 109, 142)(99, 132, 150, 190, 223)(100, 133, 172, 211, 105)(107, 140,
 179, 220, 258)(112, 147, 187, 229, 266)(116, 152, 193, 125, 163)(122,
 161, 200, 241, 123)(126, 164, 203, 245, 279)(130, 169, 209, 171,
 210)(134, 173, 213, 217, 214)(138, 176, 197, 238, 212)(143, 182, 224,
 262, 291)(148, 188, 189, 231, 269)(153, 194, 236, 154, 195)(155, 196,
 237, 276, 157)(159, 199, 240, 265, 294)(165, 204, 226, 263, 289)(167,
 206, 249, 284, 170)(175, 216, 255, 183, 225)(178, 219, 256, 290,
 307)(180, 221, 260, 181, 222)(185, 227, 205, 247, 252)(192, 234, 273,
 297, 254)(202, 243, 278, 299, 218)(208, 251, 287, 305, 239)(228, 248,
 282, 302, 312)(230, 267, 261, 232, 270)(233, 271, 296, 300, 286)(235,
 274, 298, 304, 281)(244, 253, 288, 295, 306)(246, 280, 301, 264,
 293)(250, 285, 268, 259, 272)(275, 283, 303, 292, 308)(309, 313, 310,
 311, 314),
 (1, 2)(3, 5)(4, 7)(6, 10)(8, 13)(9, 15)(11, 18)(12, 19)(14, 22)(16,
 25)(17, 27)(20, 30)(21, 32)(23, 35)(24, 36)(26, 39)(28, 42)(29,
 44)(31, 47)(33, 50)(34, 52)(37, 56)(38, 58)(40, 61)(41, 62)(45,
 66)(46, 68)(48, 71)(49, 72)(53, 77)(54, 76)(55, 80)(57, 83)(59,
 85)(60, 70)(63, 73)(64, 89)(65, 91)(67, 92)(69, 90)(74, 99)(75,
 100)(78, 103)(79, 105)(81, 107)(82, 109)(84, 102)(86, 112)(87,
 114)(88, 116)(93, 122)(94, 123)(95, 125)(96, 126)(97, 128)(98,
 130)(101, 134)(104, 138)(106, 139)(108, 124)(110, 143)(111, 145)(113,
 148)(115, 150)(117, 153)(118, 154)(119, 155)(120, 157)(121, 159)(127,
 165)(129, 167)(131, 168)(132, 170)(133, 171)(135, 136)(137, 175)(140,
 178)(141, 180)(142, 181)(144, 183)(146, 185)(147, 186)(149, 189)(151,
 179)(152, 192)(158, 197)(160, 163)(161, 172)(162, 196)(164, 202)(166,
 205)(169, 208)(173, 212)(174, 214)(176, 217)(177, 218)(182, 223)(184,
 226)(187, 228)(188, 230)(190, 232)(191, 233)(193, 215)(194, 235)(198,
 209)(199, 239)(200, 213)(201, 242)(203, 244)(204, 246)(206, 248)(207,
 250)(210, 252)(211, 253)(216, 254)(219, 236)(220, 257)(221, 259)(224,
 261)(225, 243)(227, 264)(229, 265)(231, 268)(234, 272)(237, 275)(238,
 276)(240, 277)(241, 273)(245, 278)(247, 281)(249, 283)(251, 286)(256,
 289)(258, 284)(260, 288)(262, 266)(263, 292)(269, 295)(274, 294)(279,
 287)(280, 300)(282, 301)(285, 304)(290, 306)(291, 305)(296, 309)(297,
 308)(298, 310)(299, 303)(302, 311)(307, 313)(314, 315) }

\\orbits chosen 
orbs[3]; GSet{@ 10, 88, 250, 138, 276, 229, 292, 107, 287, 244, 198, 272, 251,
 79, 241, 200, 278, 113, 204, 124, 143, 63, 223, 311, 134, 261, 158,
 44, 14, 237, 54, 30 @} 
orbs[4]; GSet{@ 13, 135, 283, 101, 31, 262, 273, 169, 289, 234, 279,
 245, 298, 188, 144, 127, 91, 73, 172, 238, 286, 213, 141, 22, 228,
 29, 197, 224, 76, 275, 62, 108 @}
\end{verbatim}}
\subsection{$J_2$ of degree 315, dimension 36: $[315,36,80]_2$}
{\small \begin{verbatim} Generators as given above. 
 \\orbit chosen
orbs[5]; GSet{@ 3, 84, 48, 313, 194, 60, 193, 191, 185, 109, 139, 300,
254, 132, 142, 295, 120, 199, 16, 36, 177, 94, 17, 53, 285, 242, 119,
78, 288, 176, 125, 192, 166, 9, 243, 99, 253, 57, 49, 137, 160, 7,
248, 140, 170, 304, 179, 264, 236, 86, 291, 220, 293, 61, 130, 75,
145, 184, 231, 32, 59, 90, 19, 64, 306, 35, 270, 93, 114, 39, 42, 218,
147, 314, 296, 277, 153, 55, 66, 129 @}
\end{verbatim}}
\subsection{Two ternary codes}
\begin{enumerate}
\item $J_1$ of degree 266: $[266,76,X]_3$
{\small \begin{verbatim}
Generators as given above.
\\orbit chosen
orbs[4],
GSet{@ 2, 4, 10, 167, 33, 3, 88, 154, 6, 149, 37, 133, 255, 258, 260,
17, 174, 15, 163, 191, 5, 77, 107, 20, 46, 152, 224, 237, 87, 41, 44,
183, 215, 245, 249, 13, 25, 254, 221, 217, 232, 266, 218, 198, 150,
128, 175, 262, 55, 8, 18, 141, 36, 116, 23, 111, 132, 207, 32, 261,
265, 243, 223, 134, 75, 216, 27, 114, 125, 160, 106, 235, 185, 182,
90, 64, 219, 117, 147, 208, 102, 247, 84, 9, 76, 137, 238, 194, 234,
227, 96, 225, 242, 157, 66, 12, 233, 139, 122, 222, 231, 197, 58, 196,
250, 193, 146, 85, 252, 172 @} 
orbs[5];
GSet{@ 14, 22, 171, 70, 43, 71, 244, 248, 170, 257, 165, 42, 35, 63,
144, 148, 95, 246, 115, 93, 112, 21, 109, 26, 226, 19, 199, 236, 80,
118, 68, 131, 97, 145, 188, 204, 92, 156, 30, 179, 34, 120, 213, 176,
31, 101, 56, 50, 98, 57, 78, 53, 79, 49, 251, 39, 259, 200, 166, 59,
110, 48, 189, 127, 28, 104, 173, 29, 168, 187, 67, 220, 16, 230, 123,
65, 142, 203, 60, 228, 129, 130, 140, 72, 105, 86, 190, 91, 73, 151,
209, 158, 205, 61, 82, 186, 47, 229, 180, 113, 210, 253, 24, 38, 195,
214, 126, 178, 108, 239, 240, 256, 169, 138, 159, 162, 51, 263, 81,
136, 103, 83, 40, 54, 94, 164, 99, 143, 192, 212, 119, 69 @}
\end{verbatim}}
\item $J_2$ of degree 100: $[100,36,16]_3$
{\small \begin{verbatim}
Generators as given
\\orbit chosen #3
orbs[3];
GSet{@ 4, 5, 44, 57, 50, 40, 8, 24, 81, 6, 52, 47, 56, 21, 68, 27, 53,
35, 46, 14, 34, 43, 22, 39, 26, 59, 10, 76, 41, 63, 74, 15, 100, 18,
33, 70, 48, 13, 17, 79, 20, 30, 72, 29, 45, 28, 67, 38, 36, 55, 69,
11, 80, 89, 16, 78, 84, 75, 82, 12, 32, 37, 58 @}
\end{verbatim}}
\end{enumerate}
\subsection{Two 5-ary codes}
\begin{enumerate}
\item $J_1$ of degree 266: $[266,56,X]_5$
{\small \begin{verbatim}
\\orbit chosen #4
orbs[4];
GSet{@ 2, 4, 15, 56, 52, 240, 23, 114, 239, 44, 104, 18, 108, 25, 97,
173, 46, 266, 85, 32, 55, 198, 206, 57, 159, 95, 121, 179, 150, 69,
130, 80, 238, 59, 185, 197, 17, 183, 154, 162, 196, 160, 81, 122, 9,
117, 47, 49, 140, 241, 36, 67, 86, 60, 263, 135, 228, 251, 73, 27,
204, 144, 257, 244, 200, 158, 99, 6, 218, 232, 202, 147, 78, 188, 20,
169, 8, 209, 254, 112, 171, 89, 207, 221, 102, 53, 109, 236, 5, 111,
195, 41, 220, 13, 155, 141, 101, 174, 33, 91, 214, 37, 12, 115, 10,
181, 105, 193, 119, 3 @}
\end{verbatim}}
\item $J_2$ of degree 315: $[315,14,180]_5$
{\small \begin{verbatim}
Generators as before
\\orbit chosen
orbs[2];
GSet{@ 2, 77, 12, 178, 89, 216, 24, 4, 271, 40 @}
\end{verbatim}}
\end{enumerate}

