Best Known (128, s)-Sequences in Base 4
(128, 129)-Sequence over F4 — Constructive and digital
Digital (128, 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
(128, 175)-Sequence over F4 — Digital
Digital (128, 175)-sequence over F4, using
- t-expansion [i] based on 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
(128, 399)-Sequence in Base 4 — Upper bound on s
There is no (128, 400)-sequence in base 4, because
- net from sequence [i] would yield (128, m, 401)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (128, 1999, 401)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41999, 401, S4, 5, 1871), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 50256 531062 054705 691460 798405 270045 721390 730516 681024 321663 131540 466982 884301 813600 991554 969593 715251 349836 634082 732887 834078 492459 292216 136599 675600 202701 646951 571319 225014 146004 200575 568226 858264 486233 023701 273988 672699 172147 860932 051285 398767 446607 048334 581499 922044 324493 502098 166296 817270 655272 551364 121265 928154 839719 501287 682053 252210 860841 162886 170082 202376 706604 085855 164772 641467 147176 711125 216202 737036 987916 584832 534265 017626 730931 103580 465610 718520 640640 797989 730110 574408 402614 580526 043880 174188 486356 041685 851629 765296 540854 802651 584287 517609 711517 402324 670240 443537 012033 702270 190488 774577 217934 165302 277346 023550 490436 586469 597614 635549 634306 226657 790767 289687 562299 636151 750543 430219 700115 119147 146381 288094 216253 260913 183727 164207 856954 609684 675564 577300 763585 020643 908365 752223 586680 871070 163041 293349 862601 884145 914580 028263 709665 696444 552943 204645 483678 487663 227147 433027 204417 593251 546208 926577 317114 656776 824471 550109 402399 388966 745280 363874 185615 725971 366447 274418 319627 031857 868466 218584 233854 926515 634162 865131 515040 476268 559546 212188 450387 635468 822935 694690 829792 851680 807374 531804 835288 255204 203561 569218 406130 027449 962027 546269 363202 882509 970149 305043 945379 548694 882597 994496 / 13 > 41999 [i]
- extracting embedded OOA [i] would yield OOA(41999, 401, S4, 5, 1871), but
- m-reduction [i] would yield (128, 1999, 401)-net in base 4, but