Best Known (22, s)-Sequences in Base 3
(22, 31)-Sequence over F3 — Constructive and digital
Digital (22, 31)-sequence over F3, using
- t-expansion [i] based on 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
(22, 53)-Sequence in Base 3 — Upper bound on s
There is no (22, 54)-sequence in base 3, because
- net from sequence [i] would yield (22, m, 55)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (22, 215, 55)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3215, 55, S3, 4, 193), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 537 389129 823333 586853 296080 335211 807839 299972 771156 980844 198119 163714 294704 099499 578360 467201 555655 223887 / 97 > 3215 [i]
- extracting embedded OOA [i] would yield OOA(3215, 55, S3, 4, 193), but
- m-reduction [i] would yield (22, 215, 55)-net in base 3, but