Best Known (41, s)-Sequences in Base 3
(41, 41)-Sequence over F3 — Constructive and digital
Digital (41, 41)-sequence over F3, using
- t-expansion [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
(41, 55)-Sequence over F3 — Digital
Digital (41, 55)-sequence over F3, using
- t-expansion [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
(41, 92)-Sequence in Base 3 — Upper bound on s
There is no (41, 93)-sequence in base 3, because
- net from sequence [i] would yield (41, m, 94)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (41, 371, 94)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3371, 94, S3, 4, 330), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 354653 782470 898582 729208 760309 092060 019323 578542 789858 618462 492562 367387 864732 444902 243350 628745 646801 486471 706952 149392 189258 292134 783728 500628 270340 405073 223308 595605 657211 543715 / 331 > 3371 [i]
- extracting embedded OOA [i] would yield OOA(3371, 94, S3, 4, 330), but
- m-reduction [i] would yield (41, 371, 94)-net in base 3, but