Best Known (1, s)-Sequences in Base 2
(1, 4)-Sequence over F2 — Constructive and digital
Digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
(1, 4)-Sequence in Base 2 — Upper bound on s
There is no (1, 5)-sequence in base 2, because
- net from sequence [i] would yield (1, m, 6)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (1, 5, 6)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 34 > 25 [i]
- m-reduction [i] would yield (1, 5, 6)-net in base 2, but