Best Known (30, s)-Sequences in Base 3
(30, 36)-Sequence over F3 — Constructive and digital
Digital (30, 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
(30, 41)-Sequence over F3 — Digital
Digital (30, 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
(30, 69)-Sequence in Base 3 — Upper bound on s
There is no (30, 70)-sequence in base 3, because
- net from sequence [i] would yield (30, m, 71)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (30, 279, 71)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3279, 71, S3, 4, 249), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1688 183989 188180 427341 259972 967797 381905 844688 872551 190547 111826 823234 339298 187164 722665 875174 834040 361066 428593 820517 049221 778799 888843 / 125 > 3279 [i]
- extracting embedded OOA [i] would yield OOA(3279, 71, S3, 4, 249), but
- m-reduction [i] would yield (30, 279, 71)-net in base 3, but