Best Known (97, s)-Sequences in Base 8
(97, 193)-Sequence over F8 — Constructive and digital
Digital (97, 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
(97, 194)-Sequence over F8 — Digital
Digital (97, 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
(97, 703)-Sequence in Base 8 — Upper bound on s
There is no (97, 704)-sequence in base 8, because
- net from sequence [i] would yield (97, m, 705)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (97, 2111, 705)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82111, 705, S8, 3, 2014), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11 228672 018456 551092 956919 638063 880792 376424 267746 929278 103392 575416 539899 415480 206535 627191 853916 685059 702691 905113 777773 191047 172895 607535 701594 344189 108628 086698 147583 866080 484690 209820 135622 714543 665860 962960 580937 814245 782324 287621 047570 336940 005755 160264 752074 279404 273534 098294 407404 891054 717808 573192 693817 760421 317444 596252 545620 425465 134339 993664 681341 242186 871879 195002 477943 282939 068502 960407 811222 847179 018241 488621 540774 771394 827103 803242 681105 966454 332285 382600 567476 576156 448037 789634 657154 004102 834247 219332 811918 318039 045101 475413 699903 581759 487527 375032 438175 907948 132301 640143 284139 484646 245921 965683 842643 271559 276443 456016 708365 141408 021424 705826 966199 142447 176195 226595 063459 507107 668422 747825 133893 953226 649163 248401 627409 633920 765010 584252 922957 425017 288978 762713 285405 614761 594863 099588 997972 031169 809123 724054 674486 775686 963322 221710 331602 911610 360581 932456 129103 678001 822974 571623 051568 811464 403519 707432 592388 438259 875200 917415 664135 150288 432198 305168 526520 164721 054893 780012 628105 153621 456257 987343 656691 087890 089585 215956 076233 434924 100076 126930 268560 914616 718608 922184 035674 376845 044518 192075 329701 026088 095843 343937 104850 352347 674624 628538 810771 697024 283668 417372 612838 715194 074576 585215 768005 556828 851909 870378 259241 249765 663002 116077 268719 204830 134604 014595 164271 754929 973776 591238 199647 442938 981981 738886 499221 751977 996560 983816 911675 115206 337751 825917 002352 290828 808800 626674 357014 599298 590052 028430 540170 677655 923953 336892 003585 668595 474044 759070 025998 651671 319241 598668 306501 323574 504344 647452 876442 059192 014844 534278 637812 242760 158275 644222 830382 569814 487659 745381 263563 158626 454274 485818 517230 459251 821119 577604 614683 457755 175156 039173 544660 818619 808004 830428 861057 854359 285263 815628 208645 575688 043729 464122 671825 426596 991132 766480 154309 517774 793464 405187 442886 825201 965077 342241 232217 385245 777335 608403 843243 784762 225551 750908 394124 120328 759032 899566 380801 649444 651008 / 403 > 82111 [i]
- extracting embedded OOA [i] would yield OOA(82111, 705, S8, 3, 2014), but
- m-reduction [i] would yield (97, 2111, 705)-net in base 8, but