Best Known (191, s)-Sequences in Base 4
(191, 199)-Sequence over F4 — Constructive and digital
Digital (191, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
(191, 257)-Sequence over F4 — Digital
Digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
(191, 589)-Sequence in Base 4 — Upper bound on s
There is no (191, 590)-sequence in base 4, because
- net from sequence [i] would yield (191, m, 591)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (191, 2949, 591)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42949, 591, S4, 5, 2758), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 987 369998 752224 938873 195214 196079 693326 457791 659721 738716 503031 835173 883419 088184 029650 377173 853086 800128 751461 125351 615911 610417 257286 409257 968820 977134 707344 200226 294905 434789 329184 947185 187964 749148 642557 868551 027211 927901 561746 684574 684573 927177 950185 530659 034125 777757 641698 368816 900621 644672 520061 940076 117707 774806 684202 065479 869088 608941 395543 882142 308965 232595 231678 525267 878332 467167 668477 314064 051480 469098 504327 288169 313423 894338 079632 559239 714422 371452 094966 097789 326495 965528 136542 482882 217657 260627 628010 867872 597740 839326 374277 660944 692590 446581 472392 854669 559628 155583 520046 416698 331621 035391 632869 264636 708009 045407 007171 327811 608816 889396 935462 901882 792220 159256 805814 841402 418740 248390 576386 292061 620820 602725 286674 070873 241982 487326 694533 393704 081733 769098 121739 710651 740097 663352 468453 636637 761501 331912 164740 017106 123222 166680 384109 478935 099573 045990 325874 960908 614843 808919 216735 266584 589753 596221 671352 816961 016501 533915 868815 093466 933012 776102 149055 614636 073256 277228 182901 894633 312127 783828 432281 272845 252756 633306 740239 824583 506877 414474 118372 663775 903019 499435 396082 002329 413429 982387 620132 977430 416147 243610 930297 880606 489590 692531 203236 102411 226930 786459 764724 172633 525712 868958 392687 901993 102603 295058 691684 795355 385249 635701 656820 223817 596116 092194 210030 251970 313249 127497 942544 637437 347578 033038 020896 886317 396811 250801 359348 920871 974351 200744 279246 688893 846853 980806 806569 954619 166784 039676 603137 911921 891366 375284 917759 984117 996529 769180 921190 468592 735481 898283 003614 566647 704890 207006 395305 776232 574912 217423 366340 287995 920468 484442 958628 530086 045904 151175 971458 323985 554561 029599 333183 108879 282435 616480 700658 077020 888313 414661 366269 095929 261887 439722 595012 928781 454994 139620 706932 288820 116162 829297 117723 526986 810953 437341 010292 683363 581952 / 2759 > 42949 [i]
- extracting embedded OOA [i] would yield OOA(42949, 591, S4, 5, 2758), but
- m-reduction [i] would yield (191, 2949, 591)-net in base 4, but