Best Known (2, s)-Sequences in Base 4
(2, 9)-Sequence over F4 — Constructive and digital
Digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
(2, 11)-Sequence in Base 4 — Upper bound on s
There is no (2, 12)-sequence in base 4, because
- net from sequence [i] would yield (2, m, 13)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (2, 16, 13)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(416, 13, S4, 3, 14), but
- the linear programming bound for OOAs shows that M ≥ 176093 659136 / 37 > 416 [i]
- extracting embedded OOA [i] would yield OOA(416, 13, S4, 3, 14), but
- m-reduction [i] would yield (2, 16, 13)-net in base 4, but