# New coverings of t-sets with (t+1)-sets: Appendix

Authors: K. J. Nurmela and P. R. J. Östergård
Title: New coverings of t-sets with (t+1)-sets
Source: Journal of Combinatorial Designs 7 (1999), 217-226 (JCD 343)

This page provides the complete Table II for the above mentioned article (only a part of the table was printed in the journal). It gives the following upper bounds for the size of covering designs (for other bounds induced by these, see the full paper):

## Table II: New covering designs

The base blocks are given in hexadecimal notation so that 0, 1, 2,..., 9, A, B,..., F correspond to the binary sequences 0000, 0001, 0010,..., 1001, 1010, 1011,..., 1111, respectively. Leading 0's are not shown, and the rightmost position is numbered 0, the leftmost n-1. The size of the orbit of a base block is shown as a superscript. The permutation group is given in brackets. For the groups, we have adopted the notation used in [L. G. Chouinard II, R. Jajcay, and S. S. Magliveras, ''Finite groups and designs,'' The CRC handbook of combinatorial designs, C. J. Colbourn and J. H. Dinitz (Editors), CRC Press, Boca Raton, 1996, pp. 587-615]. The generating permutations (in the cyclic notation) for the group are also given, since they can be constructed in many different ways. Fixed positions (if any) are those that are not listed in the generating permutations.

Bound
[Group]
Generators
Base Blocks
C(14,6,5) <= 371
[Z14]
(0,1,2,3,4,5,6,7,8,9,10,11,12,13)
3F14, D714, EB14, 15B14, 17314, 19D14, 1B514, 21F14, 27914, 29B14, 2CD14, 32B14, 35314, 36514, 45D14, 46B14, 48F14, 4E514, 53914, 54714, 5A314, 63314, 92714, 92D14, 95514, 3877, 9937, A957
C(14,9,8) <= 471
[Z5]
(0,2,4,6,8)(1,3,5,7,9)
1FF5, 2FF5, CBF5, CEF5, CFB5, D5F5, D775, DAF5, DBE5, DFA5, 147F5, 14F75, 14FD5, 157B5, 159F5, 15B75, 16AF5, 16BB5, 18DF5, 18FE5, 196F5, 197E5, 19BB5, 19DE5, 19EB5, 19EE5, 1C7D5, 1CAF5, 1CDE5, 1D575, 1D6E5, 1EAB5, 24DF5, 24FE5, 256F5, 257E5, 25BB5, 25DE5, 25EB5, 25EE5, 287F5, 28F75, 28FD5, 297B5, 299F5, 29B75, 2AAF5, 2ABB5, 2C7D5, 2CAF5, 2CDE5, 2D575, 2D6E5, 2EAB5, 30BF5, 30EF5, 30FB5, 315F5, 31775, 31AF5, 31BE5, 31FA5, 347D5, 34AF5, 34DE5, 35575, 356E5, 36AB5, 387D5, 38AF5, 38DE5, 39575, 396E5, 3AAB5, 3C3B5, 3C3E5, 3C4F5, 3C675, 3C6B5, 3C735, 3C765, 3C7A5, 3C975, 3C9B5, 3C9D5, 3CB35, 3CB55, 3CB65, 3CCD5, 3CD95, 3CE65, 3CE95, 3D5A5, 3D9A5, 3D551, 3EAA1; remove block 1FF
C(17,8,7) <= 3040
[F8,7]
(1,2,4,3,6,7,5)(9,10,12,11,14,15,13),
(0,1)(2,3)(4,5)(6,7)(8,9)(10,11)
(12,13)(14,15)
36F56, 3F556, 77356, 7AD56, 7AE56, F3656, F5356, F6556, 171756, 172B56, 173A56, 174D56, 175A56, 176556, 178E56, 179956, 17B156, 17B256, 17C356, 17D456, 17E856, 1F5156, 1F6156, 1F8A56, 1FA456, 3F1156, 3F1456, 3F4856, 1035756, 1035E56, 1037656, 103D656, 1070F56, 1073556, 1075956, 1076C56, 1079356, 107A656, 107CA56, 107F056, 10F0756, 10F7056, 1171C56, 1173856, 1174656, 1176256, 1178556, 117A156, 11F1256, 11F2456, 11F4156, 11F8856, 33F28, 3CF28, 3FC28, 3F0328, 1007F8, 17F008
C(19,5,4) <= 846
[Z18]
(0,1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17)
4F18, 7518, CB18, 11B18, 15918, 1A318, 25318, 29518, 29918, 32518, 3C118, 41718, 43918, 54318, 58918, 66118, 89318, 8C518, 91518, A2318, B0918, C0D18, CA118, E1118, 106918, 10D118, 113118, 128318, 145118, 148518, 188918, 218518, 222918, 230918, 249118, 4002D18, 4006318, 400A918, 4010718, 4019118, 4042518, 404C118, 4085118, 4092118, 4104518, 406039, 40A059, 412099, 422119
C(20,5,4) <= 1083
[Z19]
(0,1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18)
2F19, 7319, E919, 14719, 21B19, 38319, 45919, 48D19, 4C319, 4D119, 50B19, 52519, 64519, 6A119, 71119, 89519, 93119, 96119, A2319, A5119, B0519, B0919, C1319, C2919, D8119, 105519, 108719, 111319, 118919, 122919, 129119, 144919, 18A119, 194119, 1C2119, 208719, 20B119, 211519, 220D19, 224319, 232119, 424919, 442319, 8009919, 8010B19, 8015119, 801A119, 8021519, 8022919, 8040719, 8043119, 8082519, 808C119, 8090319, 8106119, 8110519, 8124119
C(22,7,6) <= 13244
[F11,10]
(1,2,4,8,5,10,9,7,3,6)
(12,13,15,19,16,21,20,18,14,17),
(0,1,2,3,4,5,6,7,8,9,10)
(11,12,13,14,15,16,17,18,19,20,21)
8E7110, 8FC110, 93E110, 979110, 182F110, 189B110, 18BA110, 18F1110, 190F110, 1A36110, 1A6A110, 1AC6110, 1B07110, 1B94110, 1C5C110, 1D15110, 381D110, 384B110, 3872110, 38A3110, 391A110, 392A110, 3961110, 3991110, 39C8110, 3A51110, 3A58110, 3A8A110, 3B0C110, 3C98110, 5827110, 5874110, 58AC110, 58C3110, 58D8110, 5926110, 5931110, 5952110, 59B0110, 5A0E110, 5A2C110, 5A61110, 5A85110, 5AA2110, 5B18110, 5B44110, 5B88110, 5C0D110, 5C32110, 5C4A110, 5C51110, 5C98110, 5CA1110, 5CC4110, 5D50110, 5D82110, 5E30110, 5E42110, 5F01110, 5F08110, 7829110, 784C110, 7885110, 7914110, 7A12110, B80E110, B813110, B82C110, B834110, B889110, B922110, BA44110, BA90110, BC09110, BD40110, BD80110, D813110, D845110, D868110, D960110, DA22110, F830110, F8C0110, 13807110, 13889110, 138B0110, 13922110, 13A03110, 13A14110, 13A28110, 13A42110, 13C41110, 13D08110, 17821110, 17940110, 17A80110, 17C10110, 1B841110, 1B860110, 1B884110, 1B910110, 1BA01110, 1BC02110, 1F804110, 27811110, 27822110, 27888110, 27A02110, 27D00110, 2E803110, 2E882110, 2E908110, 4B850110, 4F880110, 7F55, AF455, 1AE855, 1C4755, 38C555, 392555, 3AD055, 3B3055, D98455, 2E81455, 2EC8055, 3F80055, A3B22, 5B82022
C(23,8,7) <= 38962
[F23,22]
(1,5,2,10,4,20,8,17,16,11,9,22,
18,21,13,19,3,15,6,7,12,14),
(0,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22)
27F506, 57D506, 5BB506, 5CF506, 5D7506, 96F506, 9D7506, B5D506, CE7506, DA7506, E4F506, 11BB506, 11D7506, 11EB506, 12B7506, 135B506, 1375506, 13CD506, 1477506, 168F506, 16E3506, 1747506, 17A3506, 191F506, 192F506, 1A67506, 1A6B506, 1B17506, 1B87506, 215F506, 21BD506, 22D7506, 232F506, 23AB506, 23CB506, 24AF506, 24F9506, 2537506, 25E3506, 261F506, 2753506, 2787506, 287B506, 28DD506, 29D3506, 2AE3506, 2C57506, 2D47506, 2E2B506, 34C7506, 416F506, 419F506, 41B7506, 433D506, 43E5506, 44CF506, 46D5506, 46F1506, 49CB506, 49E9506, 4AAB506, 4B33506, 4F15506, 4F43506, 5317506, 5395506, 54D5506, 564D506, 5953506, 865D506, 8DC3506, 9553506, 9D23506, A497506, 102EB506, FF253, 37B253, 1CA7253, 352B253
C(24,7,6) <= 23276
[F23,22]
(1,5,2,10,4,20,8,17,16,11,9,22,
18,21,13,19,3,15,6,7,12,14),
(0,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22)
19F506, 277506, 2CF506, 34F506, 4BB506, 4F5506, 6C7506, 83F506, 8E7506, 9B5506, B17506, C97506, 10B7506, 11E9506, 123D506, 130F506, 1563506, 1587506, 1617506, 1663506, 1917506, 1A87506, 20BB506, 2179506, 2437506, 2457506, 2695506, 26A3506, 322B506, 4297506, 80006F506, 80021F506, 800533506, 800547506, 800927506, 800939506, 800953506, 800C87506, 80108F506, 801171506, 8020E9506, 17D253, 1D7253, 727253, 1C47253, 80016D253, 8002B5253, 8002CD253, 80058D253, 80068B253, 8008F1253
C(25,8,7) <= 78012
[L2]
(0,10,9,8,7,6,5,4,3,2,1)
(12,22,21,20,19,18,17,16,15,14,13),
(0,11)(1,10)(2,5)(3,7)(4,8)(6,9)(12,23)
(13,22)(14,17)(15,19)(16,20)(18,21)
305F660, 30BD660, 3137660, 316B660, 317C660, 31BA660, 31D6660, 31D9660, 331D660, 332E660, 33B4660, 347A660, 34DC660, F03A660, F05C660, F071660, F096660, F0A9660, F0C5660, F115660, F12C660, F149660, F162660, F18A660, F1A4660, F1B0660, F1C2660, F21C660, F289660, F291660, F2D0660, F2E0660, F312660, F321660, F416660, F483660, F48C660, F4A8660, F4C1660, F550660, F682660, F8A2660, F981660, FA90660, 1F00D660, 27039660, 27056660, 2708B660, 2709C660, 270C5660, 270D1660, 27158660, 271B0660, 27213660, 27292660, 27415660, 2741A660, 27609660, 27628660, 27650660, 3F042660, 3F104660, 3F220660, 5F022660, 6F012660, 7700A660, 7B006660, 7D005660, 7D00C660, 7D018660, 7D082660, 7D102660, 7D202660, 100007F660, 100107B660, 100311D660, 1003169660, 10031D2660, 1003334660, 1003478660, 10034D4660, 100700F660, 1007017660, 1007027660, 100703C660, 1007059660, 100706A660, 10070E4660, 100714A660, 1007191660, 1007258660, 1007289660, 1007344660, 1007530660, 1007921660, 1007930660, 100F098660, 100F0A1660, 100F211660, 100F230660, 100F282660, 100F380660, 100F482660, 100F490660, 101F028660, 1027007660, 1027049660, 10270D0660, 1027411660, 102F006660, 102F024660, 102F050660, 102F101660, 102F208660, 102F600660, 102F880660, 107F000660, 364E132, 5F240132, 13F008132, 100013F132, 100117C132, 101F240132
C(26,8,7) <= 105000
[F25,24]
(1,5,23,22,17,24,2,10,16,19,9,18,
4,20,7,8,13,6,3,15,14,11,21,12),
(0,1,2,3,4)(5,6,7,8,9)(10,11,12,13,14)
(15,16,17,18,19)(20,21,22,23,24)
5EE600, 6BB600, 6DE600, 6ED600, 79B600, 7B6600, 7F1600, C3F600, CF5600, D5E600, D79600, DC7600, DCD600, DF2600, ED6600, FAA600, 14F9600, 1576600, 15BC600, 15D3600, 165B600, 1697600, 170F600, 178E600, 1C6D600, 1C8F600, 1D59600, 1D8B600, 1F15600, 2C57600, 2D3A600, 849F600, 84D7600, 84FA600, 853D600, 854F600, 85A7600, 85B3600, 85D5600, 85D9600, 85EA600, 85F4600, 8667600, 86F8600, 8735600, 8772600, 8787600, 87A9600, 87D2600, 88CF600, 88F3600, 88FC600, 89BC600, 8A1F600, 8A79600, 8AAE600, 8B2B600, 8B66600, 8B96600, 8BC9600, 8C5D600, 8D78600, 8D8B600, 8DE4600, 8E2E600, 8E87600, 8F45600, 8F4A600, 8FD0600, 9077600, 90EB600, 91EC600, 923B600, 928F600, 92CD600, 935C600, 945E600, 95B1600, 95C6600, 9655600, 9672600, 96AA600, 96E1600, 9725600, 98F1600, 9917600, 994D600, 99A3600, 9A2D600, 9A36600, 9A4E600, 9A53600, 9AE8600, 9B1C600, 9B2A600, 9C53600, 9D0E600, 9DA2600, 9F48600, A1DA600, A36A600, A3D4600, A475600, A5E1600, A63A600, A6E2600, A770600, A91D600, AB61600, B0D6600, B1B4600, B263600, B4D1600, BAC2600, 200047B600, 20004BE600, 20004CF600, 2000557600, 200057C600, 2000597600, 2000637600, 200063E600, 200069D600, 20006D3600, 200070F600, 2000759600, 200075A600, 20007A5600, 2000C7A600, 2000CAD600, 2000D1B600, 2000D2B600, 2000D8B600, 2000EA9600, 2001437600, 200145E600, 200146E600, 20014F2600, 2001C36600, 2001D0D600, 200843E600, 2008476600, 20084F1600, 20085B8600, 200864E600, 200866A600, 2008699600, 20086D4600, 2008726600, 2008758600, 200885B600, 2008876600, 200889E600, 200894E600, 20089C6600, 2008ACA600, 2008AE1600, 2008B58600, 2008C5A600, 2009196600, 20092B8600, 1F7300, EE3300, 15EA300, 17C9300, 1C73300, 1E3C300, 1E59300, 1E93300, 2E8B300, 9E62300, ADA8300, AEA1300, 20007E2300, 20007E8300, 20007F0300, 2000CE6300, 2000D63300, 2000DB1300, 2000DD8300, 2000E71300, 2000EB8300, 2000ECC300, 2000F46300, 20014E5300, 20015D4300, 2001669300, 200172A300, 2001792300
C(27,5,4) <= 3848
[Z26]
(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25)
6D26, 12726, 14D26, 19926, 21D26, 36126, 47126, 4C526, 61326, 64926, 78126, 88D26, 8B126, 91326, A0726, D0926, 115126, 12A126, 142926, 182326, 205926, 20C326, 216126, 221326, 230526, 241526, 284526, 2A8126, 2E0126, 300B26, 302526, 308526, 350126, 412926, 424526, 428926, 430326, 441926, 44A126, 460526, 481526, 484326, 4A2126, 4D0126, 500D26, 501326, 50C126, 560126, 602326, 610526, 720126, 802D26, 804B26, 80E126, 829126, 842326, 880726, 8A4126, 910526, 941126, 980926, A0A126, A40926, A90126, B04126, C08326, C81126, E00926, 100A326, 1014926, 1018526, 1024326, 1049126, 1081926, 1103126, 1120926, 1188126, 1211126, 1421126, 1444126, 1804526, 1850126, 1882126, 1A20126, 1C10126, 2044326, 2052126, 2068126, 2086126, 2088526, 20A0926, 2101526, 2108326, 2124126, 2220526, 2248126, 2406126, 2418126, 2830126, 3040926, 3110126, 4044926, 4062126, 4080B26, 40C0526, 4101926, 4112126, 4220926, 4281126, 4810926, 4908126, 5020526, 5104126, 8181126, 8209126, 8210926, 8222126, 8408526, 8824126, A084126, 400003926, 400006326, 40000A526, 400018326, 400020B26, 400042526, 400054126, 400098126, 4000C0326, 400104526, 400108926, 4001A0126, 400409126, 400448126, 400482126, 400510126, 400811126, 400920126, 400C04126, 401012126, 401028126, 401040326, 401080526, 402022126, 404084126, 400600313, 400A00513, 401200913, 402201113, 404202113, 408204113
C(27,6,5) <= 15210
[F27,26]
(1,3,9,5,15,23,13,17,20,4,12,14,11,2,
6,18,7,21,16,26,22,10,8,24,25,19),
(0,1,2)(3,4,5)(6,7,8)(9,10,11)(12,13,14)
(15,16,17)(18,19,20)(21,22,23)(24,25,26)
77702, 24F702, 366702, 39A702, 6A9702, 715702, E52702, 125C702, 126A702, 12AA702, 12B4702, 1319702, 142E702, 14B2702, 14CA702, 1543702, 1570702, 158C702, 188B702, 161A351, 1683351, 16D0351, 1C1C351, 3384351, DB117
C(27,7,6) <= 50895
[F27,26]
(1,3,9,5,15,23,13,17,20,4,12,14,11,2,
6,18,7,21,16,26,22,10,8,24,25,19),
(0,1,2)(3,4,5)(6,7,8)(9,10,11)(12,13,14)
(15,16,17)(18,19,20)(21,22,23)(24,25,26)
23F702, 3AB702, 3F8702, 675702, 6BC702, 6D9702, 6DA702, 787702, 7A9702, 7B2702, E1B702, E5C702, EE8702, 12AB702, 12B5702, 134E702, 1399702, 13A6702, 149B702, 151D702, 1571702, 15C3702, 161E702, 1627702, 163A702, 16C5702, 16E2702, 178C702, 17D0702, 19C5702, 1A55702, 1AC9702, 1B32702, 1BA1702, 1C59702, 1CCA702, 1E61702, 1E62702, 1F09702, 1F24702, 3256702, 3265702, 330B702, 3389702, 344E702, 3463702, 349C702, 34AA702, 34CC702, 3591702, 389A702, 3925702, 3949702, 72A2702, 730C702, 7321702, 9266702, 9472702, 950B702, 9B0A702, AC62702, 40B2A702, 40E51702, DF351, EF351, 4024F351, 402A7351, 40317351, 40359351, 403B1351, 40457351, 4048F351, 404DC351, 40574351, 405AC351, 40867351, 408F2351, 4090F351, 4099A351, 41A43351, 43341351, 44685351
C(27,9,8) <= 334854
[A\GammaL1(27)]
(0,1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17)
(18,19,20,21,22,23,24,25,26),
(0,26,18,13,8,19)(1,16,20,15,6,5)
(2,10,14,23,3,11)(4,7,25,12,9,21)(22,24)
3BF2106, 7DE2106, 7E72106, 7ED2106, B5F2106, B7D2106, BEB2106, EF92106, F762106, FAE2106, 13EB2106, 16CF2106, 16DD2106, 16F62106, 177A2106, 17D32106, 1AD72106, 1AED2106, 1AF32106, 1B3E2106, 1B4F2106, 1BAD2106, 1BF82106, 1EAB2106, 1F1B2106, 1F3C2106, 1F632106, 1F692106, 1FC52106, 22FB2106, 26FA2106, 27762106, 279D2106, 27E32106, 27EC2106, 2A6F2106, 2AF52106, 2BD32106, 2BD92106, 2E732106, 2E7C2106, 2ECD2106, 2EE32106, 2F392106, 2F6A2106, 325F2106, 329F2106, 32E72106, 32FC2106, 36B62106, 36B92106, 36E92106, 372D2106, 379A2106, 3A3E2106, 3A6D2106, 3ACE2106, 3B1E2106, 3B352106, 3B722106, 3B9C2106, 3E272106, 3E2B2106, 3EB42106, 3ED22106, 3EE42106, 3F0E2106, 3F252106, 3F542106, 3F642106, 3F832106, 46F92106, 476E2106, 4A772106, 4BB32106, 4E4F2106, 4ED52106, 4F5A2106, 52DB2106, 52EE2106, 53972106, 53DC2106, 56D32106, 571E2106, 57E42106, 5A7C2106, 5B652106, 5E352106, 5E562106, 5E6A2106, 5E932106, 5F262106, 5F432106, 5FD02106, 66792106, 67782106, 67B22106, 6AD32106, 6AD62106, 6B692106, 6B742106, 6ECA2106, 6ED12106, 6F382106, 725E2106, 72DA2106, 73AC2106, 73E22106, 762E2106, 764B2106, 77322106, 77452106, 774A2106, 77542106, 77832106, 7A272106, 7A552106, 7A592106, 7A952106, 7E622106, 7E922106, 7F882106, 926F2106, 96DA2106, 97472106, 97552106, 97B42106, 9E392106, 9ED22106, 9F982106, 9FA22106, AE952106, AEA52106, AED82106, B7232106, B7252106, BAE12106, BF122106, CECC2106, CF072106, CF912106, EEC12106, F7902106, FA0E2106, 1564E2106, 156B22106, 16E8C2106, 16F812106, 40E572106, 412F92106, 4171E2106, 417352106, 4196D2106, 41D272106, 4235E2106, 458DA2106, 469E42106, 4873C2106, 494F22106
C(28,5,4) <= 4550
[Z26]
(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25)
F126, 18B26, 29326, 2A926, 44B26, 49526, 52926, 5C126, 83926, 88D26, 8C926, 9A126, B0926, C2326, 106526, 10A326, 120726, 122926, 168126, 180B26, 190526, 191126, 1C0926, 202B26, 205326, 226126, 231126, 24A126, 250526, 260326, 288326, 303126, 310326, 320526, 403326, 409926, 414526, 425126, 430526, 482526, 503126, 504326, 508526, 510926, 601526, 618126, 620926, 6A0126, 740126, 801B26, 803526, 815126, 824926, 829126, 862126, 880726, 8D0126, 918126, 940326, A14126, B00926, C60126, E02126, 1018526, 1020B26, 1040726, 1048926, 1086126, 10E0126, 1101326, 1120526, 1150126, 1184126, 120C126, 1241126, 140A126, 1444126, 1480326, 1808326, 1814126, 2010D26, 2024326, 2032126, 2040D26, 2050326, 2085126, 2098126, 2109126, 2204526, 2280926, 2404926, 240C126, 2441126, 280A126, 2820526, 2844126, 2904126, 3410126, 4042926, 4044526, 40C1126, 4121126, 4204926, 4228126, 4241126, 4410326, 4488126, 4812126, 5022126, 6082126, 8106126, 8411126, 8422126, 8440926, 8484126, 8882126, 400002726, 400006926, 400014326, 400021526, 400021926, 40002C126, 400045126, 400060926, 4000A0326, 400112126, 400141126, 400188126, 400440526, 400481126, 400830126, 400884126, 400900526, 400C08126, 401042126, 401090126, 402011126, 402040326, 402100926, 404080926, 404104126, 800004726, 800005926, 800013126, 800020D26, 800030326, 8000A8126, 800108926, 800114126, 800140526, 800182126, 800202526, 800208926, 800284126, 800428126, 800442126, 800480326, 800520126, 800604126, 800806126, 800848126, 800901126, 800C10126, 801024126, 802020326, 802044126, C00009126, C00010526, C00080526, C000C0126, C00210126, C00401126, 400600313, 400A00513, 401200913, 404202113, 408204113, 802201113
C(28,6,5) <= 18369
[F27,26]
(1,3,9,5,15,23,13,17,20,4,12,14,11,2,
6,18,7,21,16,26,22,10,8,24,25,19),
(0,1,2)(3,4,5)(6,7,8)(9,10,11)(12,13,14)
(15,16,17)(18,19,20)(21,22,23)(24,25,26)
77702, 695702, 70D702, 732702, 746702, 758702, E49702, E54702, E62702, 121E702, 122B702, 1436702, 14E8702, 1570702, 1788702, 18D1702, 9254702, 9262702, A862702, 800022D702, 80002D1702, 8000394702, 8000709702, 80012E0702, 1C2A351, 800004F351, 800005D351, 800006B351, DB117
C(28,7,6) <= 65286
[F27,26]
(1,3,9,5,15,23,13,17,20,4,12,14,11,2,
6,18,7,21,16,26,22,10,8,24,25,19),
(0,1,2)(3,4,5)(6,7,8)(9,10,11)(12,13,14)
(15,16,17)(18,19,20)(21,22,23)(24,25,26)
2EE702, 2F5702, 3B6702, 62F702, 66D702, 673702, 69E702, 72D702, 753702, 759702, 7C6702, 7E1702, E55702, EC6702, EE8702, 1237702, 12C7702, 12E9702, 1395702, 13B1702, 145B702, 1547702, 15B2702, 161B702, 1669702, 16CA702, 1762702, 17D0702, 1879702, 18F4702, 192D702, 196A702, 19A5702, 19C6702, 1A55702, 1A99702, 1B16702, 1B23702, 1C96702, 1CE4702, 1D49702, 1D64702, 1EA1702, 1F0C702, 32A5702, 3386702, 3389702, 348E702, 34E8702, 3519702, 3551702, 384B702, 38A3702, 7249702, 7252702, 72A2702, 95A4702, A866702, 4046B702, 406A5702, 408B3702, 40B51702, 40E61702, 4144D702, 41F04702, 80000DD702, 800023D702, 8000257702, 80002F8702, 8000327702, 80003E2702, 80006A9702, 80006C3702, 80006E4702, 8000713702, 8000758702, 8000E4C702, 8001271702, 800131A702, 80013C4702, 8001472702, 8001561702, 8001585702, 800168C702, 800188B702, 8001C92702, 7F351, 40317351, 4048F351, 404DC351, 40574351, 40867351, 411E2351, 41A43351, 8001629351, 8001634351, 80017A0351, 8001A86351, 8001B60351, 8001C2A351
C(28,9,8) <= 470340
[A\GammaL1(27)]
(0,1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17)
(18,19,20,21,22,23,24,25,26),
(0,26,18,13,8,19)(1,16,20,15,6,5)
(2,10,14,23,3,11)(4,7,25,12,9,21)(22,24)
3BF2106, 7F62106, B772106, BEE2106, EDD2106, EEB2106, EF92106, F2F2106, F5E2106, F972106, F9B2106, FE32106, 127F2106, 12FD2106, 13F32106, 17762106, 17AB2106, 17D92106, 1AB72106, 1ADB2106, 1AF62106, 1B2F2106, 1B6E2106, 1BB92106, 1BF82106, 1E6B2106, 1EE62106, 1F552106, 1F692106, 1F8D2106, 1FAC2106, 23EE2106, 26BD2106, 27BC2106, 27D32106, 2A7D2106, 2AFC2106, 2B6B2106, 2E5B2106, 2E672106, 2EDC2106, 2F172106, 2F392106, 2F4D2106, 2F742106, 2F9A2106, 2FCC2106, 32E72106, 33372106, 333E2106, 362F2106, 36AD2106, 3A7C2106, 3ACE2106, 3AD52106, 3BE22106, 3E712106, 3E9C2106, 3EA52106, 3F0B2106, 3F322106, 3F462106, 3FE02106, 47672106, 4AD72106, 4B372106, 4B7C2106, 4E6D2106, 4E732106, 4F712106, 4F932106, 4FB42106, 4FC62106, 4FC92106, 52CF2106, 539D2106, 56792106, 57532106, 57CC2106, 57D42106, 5A4F2106, 5A572106, 5A6E2106, 5A7C2106, 5B652106, 5BCC2106, 5EAA2106, 5ED12106, 5F0E2106, 5F622106, 67B22106, 67E82106, 6A7A2106, 6AF12106, 6AF22106, 6B712106, 6B722106, 6EE42106, 6F4C2106, 723D2106, 725E2106, 73962106, 73D82106, 761E2106, 76A62106, 770D2106, 77A82106, 7A2E2106, 7A592106, 7AB42106, 7B1C2106, 7B942106, 7E492106, 7E8A2106, 7EC42106, 7EC82106, 925F2106, 96DA2106, 9A9E2106, 9B9A2106, 9BE42106, AED42106, AF852106, AFA12106, B6A32106, B7252106, BAA62106, BB072106, BE342106, BF112106, CE4E2106, CE782106, CF1A2106, CF262106, CF542106, CFA22106, D7382106, D78A2106, D7922106, EEC12106, F7C02106, FAE02106, 156B22106, 407C72106, 40B6D2106, 40E572106, 411CF2106, 4129F2106, 417352106, 41CF22106, 458CB2106, 458EA2106, 800037E2106, 800039F2106, 80003DB2106, 800066F2106, 80006BB2106, 80007572106, 80007792106, 80007B52106, 80007DC2106, 8000A3F2106, 8000AF52106, 8000B4F2106, 8000E752106, 8000EA72106, 8000EBC2106, 8000EE92106, 8000F2D2106, 8000F532106, 8000FF02106, 80012BB2106, 800139B2106, 80016B92106, 80016D62106, 800171D2106, 800174B2106, 800176C2106, 80017E12106, 80017E42106, 8001A5D2106, 8001A6E2106, 8001ACB2106, 8001AF82106, 8001B742106, 8001E932106, 8001EC92106, 8001F072106, 8001F1A2106, 8001F232106, 8001F252106, 8001FC12106, 80023AD2106, 800269E2106, 80027632106, 80027992106, 8002AD32106, 8002BB42106, 8002E332106, 8002E6C2106, 8002F322106, 8002F452106, 8002F582106, 80036692106, 80037702106, 80037A42106, 8003A652106, 8003A722106, 8003EA22106, 8003F282106, 8003F412106, 8003F422106, 80046CB2106, 800474D2106, 8004F342106, 800565A2106, 8005A692106, 8005A932106, 8005F122106, 800664E2106, 8006AF02106, 800BA342106, 800CFC02106, 8005BC8702