Best Known (230, s)-Sequences in Base 2
(230, 84)-Sequence over F2 — Constructive and digital
Digital (230, 84)-sequence over F2, using
- base reduction for sequences [i] based on digital (73, 84)-sequence over F4, using
- s-reduction based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- s-reduction based on digital (73, 103)-sequence over F4, using
(230, 128)-Sequence over F2 — Digital
Digital (230, 128)-sequence over F2, using
- t-expansion [i] based on digital (215, 128)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 215 and N(F) ≥ 129, using
(230, 240)-Sequence in Base 2 — Upper bound on s
There is no (230, 241)-sequence in base 2, because
- net from sequence [i] would yield (230, m, 242)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (230, 1925, 242)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21925, 242, S2, 8, 1695), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 205137 673590 504545 435814 905583 111535 179895 736570 919852 164450 065674 063959 179263 433170 228500 801973 586834 933569 512518 036582 663130 157343 806833 632170 563120 945752 966292 919191 013547 201229 465774 577551 544890 276159 062427 049287 315777 673377 821257 475697 575229 087689 042711 501271 952384 926187 160297 234457 788997 528284 793241 016947 474413 530474 968358 184465 258247 148696 639612 671856 707112 093201 039253 107442 323541 658956 375149 910697 634854 093322 519719 211839 247054 144108 036059 739948 651960 036128 097024 361775 701175 297594 438734 335215 971168 824254 438835 418458 080834 293361 749869 021276 339568 985912 847626 238332 764160 / 53 > 21925 [i]
- extracting embedded OOA [i] would yield OOA(21925, 242, S2, 8, 1695), but
- m-reduction [i] would yield (230, 1925, 242)-net in base 2, but