Best Known (125, s)-Sequences in Base 4
(125, 129)-Sequence over F4 — Constructive and digital
Digital (125, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
(125, 175)-Sequence over F4 — Digital
Digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
(125, 390)-Sequence in Base 4 — Upper bound on s
There is no (125, 391)-sequence in base 4, because
- net from sequence [i] would yield (125, m, 392)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (125, 1954, 392)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41954, 392, S4, 5, 1829), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 979 649843 668151 127959 984797 977106 898474 757371 716960 434208 162928 340053 686793 600239 129312 949208 205966 265562 161678 289054 357875 018614 907795 999175 672544 456522 596863 594322 189051 770420 736303 774347 398367 914639 775109 452584 213903 051017 209874 251585 856353 722530 813037 915335 219822 339939 620493 757243 476522 838788 369422 689999 479608 362873 803051 259527 738818 304958 811925 571417 163003 906409 147866 570900 878234 280646 355732 908311 135258 537782 910197 900202 024512 073898 709071 589064 722615 696651 704688 676854 986956 585315 075863 206738 861619 632574 793929 663828 581059 262736 279299 873851 868351 438522 345013 446102 803644 966797 304199 851471 867990 665784 086727 708303 563472 520072 489650 632024 500066 156396 029348 321521 347991 781978 006880 170238 168961 648249 365555 578408 750217 364707 154282 840123 490186 623732 178094 213491 323737 450812 246274 590849 746480 352675 858578 389891 337315 764141 607427 300394 242048 243867 384313 227112 407457 114294 253372 868813 901306 167525 553236 975083 776896 194001 504478 269530 369936 502669 035514 069278 489553 816671 075219 452492 536352 520171 557044 185231 801845 440224 415969 865532 497832 819460 044254 644211 535631 070939 021213 751744 233003 525491 486405 392672 385555 672049 855559 464970 787659 577464 296800 846363 128454 903669 078495 762954 846208 / 305 > 41954 [i]
- extracting embedded OOA [i] would yield OOA(41954, 392, S4, 5, 1829), but
- m-reduction [i] would yield (125, 1954, 392)-net in base 4, but