Best Known (31, s)-Sequences in Base 3
(31, 36)-Sequence over F3 — Constructive and digital
Digital (31, 36)-sequence over F3, using
- t-expansion [i] based on digital (28, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 28 and N(F) ≥ 37, using
(31, 41)-Sequence over F3 — Digital
Digital (31, 41)-sequence over F3, using
- t-expansion [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(31, 72)-Sequence in Base 3 — Upper bound on s
There is no (31, 73)-sequence in base 3, because
- net from sequence [i] would yield (31, m, 74)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (31, 290, 74)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3290, 74, S3, 4, 259), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 229 508652 590225 900915 193766 377529 564949 108466 983495 168600 256377 208056 541526 061551 978631 651838 527412 783227 454480 502657 288667 678716 723464 947451 / 65 > 3290 [i]
- extracting embedded OOA [i] would yield OOA(3290, 74, S3, 4, 259), but
- m-reduction [i] would yield (31, 290, 74)-net in base 3, but