Best Known (108, s)-Sequences in Base 7
(108, 88)-Sequence over F7 — Constructive and digital
Digital (108, 88)-sequence over F7, using
- Niederreiter–Xing sequence construction III based on function field F2/F7 with g(F2) = 21, N(F2) ≥ 2, and N(F2) + N2(F2) ≥ 89 from GarcÃa–Stichtenoth tower as constant field extension [i]
(108, 104)-Sequence over F7 — Digital
Digital (108, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
(108, 671)-Sequence in Base 7 — Upper bound on s
There is no (108, 672)-sequence in base 7, because
- net from sequence [i] would yield (108, m, 673)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (108, 2015, 673)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(72015, 673, S7, 3, 1907), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 175790 055863 924405 753593 718663 665009 584973 605078 773107 188736 287774 125779 486303 644622 436745 860409 850267 751354 006130 268220 633938 083860 813999 114326 613803 358190 812417 722058 121839 506441 959754 606229 909025 608293 513970 185972 230837 091647 561582 748532 511843 028539 652469 678556 969906 425320 001547 332938 197806 384817 872885 268735 280418 141076 085651 426756 130722 171829 487335 683233 164685 100258 616103 245823 587524 411492 107012 058144 492331 998480 825922 062452 410841 981193 255131 618878 418405 257417 193779 724442 413507 993319 118283 163910 766585 968767 143389 717046 680363 650867 183925 409278 186493 806533 848795 522468 728681 449977 702007 504837 934866 964178 292777 106028 351145 200347 728092 897040 021113 364525 949132 975465 487861 509850 690226 455825 049367 168243 193653 977497 172925 410501 228025 221647 877262 938665 995988 400817 902610 655293 422589 636183 444584 568706 396922 751214 975983 696916 145234 903769 330490 822819 354348 698550 570623 284638 882486 167709 744254 527782 834544 723661 584349 954020 520464 630914 798186 637838 977558 419493 611658 248137 059789 426719 432025 114570 435051 979431 070370 642005 498689 047593 940724 027618 887200 980935 942934 986680 766703 271945 308033 484143 659153 826438 454316 808784 285865 856204 562985 162279 228258 339204 902924 393926 027428 249268 447612 953856 286825 055998 903227 617618 130444 512734 478447 053228 887043 541439 732249 122308 440204 309534 244835 568800 188153 935030 515398 307739 684818 341144 787194 410412 780493 409552 074297 945731 510735 405249 697446 125763 752216 063264 513748 406684 479823 361489 579860 949711 329774 264821 131824 138519 491993 905941 807741 342149 351722 762454 129153 052166 691203 020218 775138 484908 786416 797040 196314 688740 690254 885947 026278 534318 202977 346699 925280 000653 354464 879561 439810 406643 023010 103725 005014 649105 782598 360380 488549 227775 736896 497529 944735 814655 320094 156808 / 53 > 72015 [i]
- extracting embedded OOA [i] would yield OOA(72015, 673, S7, 3, 1907), but
- m-reduction [i] would yield (108, 2015, 673)-net in base 7, but