Best Known (104, s)-Sequences in Base 8
(104, 193)-Sequence over F8 — Constructive and digital
Digital (104, 193)-sequence over F8, using
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 85 and N(F) ≥ 194, using
(104, 194)-Sequence over F8 — Digital
Digital (104, 194)-sequence over F8, using
- t-expansion [i] based on digital (77, 194)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 77 and N(F) ≥ 195, using
(104, 753)-Sequence in Base 8 — Upper bound on s
There is no (104, 754)-sequence in base 8, because
- net from sequence [i] would yield (104, m, 755)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (104, 2261, 755)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82261, 755, S8, 3, 2157), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 101940 925910 826864 253537 297136 442606 910053 848504 395437 928709 647343 362673 183101 894382 615773 600326 551808 263470 849689 672783 905576 126217 444387 375118 022585 162507 117456 550554 289138 121043 887364 947137 897520 595946 367075 161823 641628 107070 578967 011955 446240 424520 881188 865925 962176 473570 380041 022167 089751 257139 058448 696706 757260 551581 249780 154309 886683 055929 261186 460605 502747 356297 924608 729665 943847 279487 206941 694003 386951 715997 128556 896037 700337 181455 876724 295191 129761 364927 942456 332611 633201 707393 704128 288980 830202 967247 154816 815041 068716 548696 826220 758854 825770 396056 802742 004433 849853 499266 515032 191485 022295 593883 811650 632709 566632 536346 980046 698579 406535 296755 278550 876512 792623 706550 989509 252679 636003 838002 757990 688096 110569 922131 619000 321515 191020 292113 865049 026645 013475 152782 963592 080408 931721 805557 451871 708907 927570 138234 017213 304618 861449 929961 697858 068816 852764 874227 470615 278449 471462 930787 415671 533314 508260 613472 042021 116284 599148 657097 250721 811135 822184 200149 315005 117688 319753 508363 663774 164050 397895 921951 704193 877558 435594 549931 962121 002553 161501 718224 375643 464247 150863 338528 094291 233781 154676 147324 783244 525324 798667 638986 635858 966937 838589 668409 770795 754366 131152 724463 721137 011631 202614 790441 388244 094713 201397 531458 742728 906666 799308 644241 536838 580838 513449 048072 831988 151519 054064 882403 941619 416317 553168 368377 980496 976066 908253 746828 286248 763116 782278 448816 894414 759026 562411 746584 047679 306708 070382 158917 213150 717781 033873 887955 171608 155563 435602 360964 258135 567231 903139 521017 064950 263519 889713 232891 423036 505567 968494 942995 078894 838301 950935 948860 359904 261846 858457 775326 876324 575017 155483 412739 477605 808459 797867 421071 458553 400425 626848 794302 442725 378887 699597 152723 373244 597913 077554 401866 663099 209908 004948 991127 255599 441204 344297 705487 237472 892519 261289 228261 687926 976483 091060 696731 147575 453785 630140 389159 739015 715959 186099 403823 686787 631407 372405 895733 979485 313064 215775 003825 325498 522437 314471 739410 419320 685889 486463 397506 401515 213253 880635 329738 362428 400351 025039 275361 499012 829292 977288 673819 949155 026250 760192 / 1079 > 82261 [i]
- extracting embedded OOA [i] would yield OOA(82261, 755, S8, 3, 2157), but
- m-reduction [i] would yield (104, 2261, 755)-net in base 8, but