Best Known (30, s)-Sequences in Base 9
(30, 77)-Sequence over F9 — Constructive and digital
Digital (30, 77)-sequence over F9, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
(30, 109)-Sequence over F9 — Digital
Digital (30, 109)-sequence over F9, using
- t-expansion [i] based on digital (26, 109)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 26 and N(F) ≥ 110, using
(30, 263)-Sequence in Base 9 — Upper bound on s
There is no (30, 264)-sequence in base 9, because
- net from sequence [i] would yield (30, m, 265)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (30, 527, 265)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9527, 265, S9, 2, 497), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 688392 129341 622431 958587 720392 607339 651930 719889 089788 476677 497278 437027 455142 897879 045860 695649 496654 224516 741638 311106 749038 159228 967290 586480 334952 422260 487825 043131 276768 746493 440893 687073 226171 649590 496329 260984 688353 954687 602573 963961 574128 948969 276521 365989 525774 885623 212894 487546 505720 779675 155178 091834 033235 853739 520032 346482 413309 623395 875185 622193 681640 449087 392083 146599 222459 509113 351635 298802 269558 232137 514879 772740 790271 372948 290320 285640 591625 204960 629519 612944 069377 992658 087963 604703 / 83 > 9527 [i]
- extracting embedded OOA [i] would yield OOA(9527, 265, S9, 2, 497), but
- m-reduction [i] would yield (30, 527, 265)-net in base 9, but