Best Known (0, s)-Sequences in Base 256
(0, 256)-Sequence over F256 — Constructive and digital
Digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
(0, 256)-Sequence in Base 256 — Upper bound on s
There is no (0, 257)-sequence in base 256, because
- net from sequence [i] would yield (0, m, 258)-net in base 256 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 258)-net in base 256, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 256m ≥ 65791 > 2562 [i]
- m-reduction [i] would yield (0, 2, 258)-net in base 256, but