Best Known (2, s)-Sequences in Base 2
(2, 5)-Sequence over F2 — Constructive and digital
Digital (2, 5)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 2 and N(F) ≥ 6, using
(2, 5)-Sequence in Base 2 — Upper bound on s
There is no (2, 6)-sequence in base 2, because
- net from sequence [i] would yield (2, m, 7)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (2, 10, 7)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(210, 7, S2, 3, 8), but
- the linear programming bound for OOAs shows that M ≥ 1 314304 / 1193 > 210 [i]
- extracting embedded OOA [i] would yield OOA(210, 7, S2, 3, 8), but
- m-reduction [i] would yield (2, 10, 7)-net in base 2, but