Best Known (21, s)-Sequences in Base 3
(21, 31)-Sequence over F3 — Constructive and digital
Digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
(21, 51)-Sequence in Base 3 — Upper bound on s
There is no (21, 52)-sequence in base 3, because
- net from sequence [i] would yield (21, m, 53)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (21, 207, 53)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3207, 53, S3, 4, 186), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 165555 871196 388364 355015 704118 291262 504527 064871 597522 368472 700777 167654 116327 144149 485010 990630 603295 / 187 > 3207 [i]
- extracting embedded OOA [i] would yield OOA(3207, 53, S3, 4, 186), but
- m-reduction [i] would yield (21, 207, 53)-net in base 3, but