Best Known (0, s)-Sequences in Base 32
(0, 32)-Sequence over F32 — Constructive and digital
Digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
(0, 32)-Sequence in Base 32 — Upper bound on s
There is no (0, 33)-sequence in base 32, because
- net from sequence [i] would yield (0, m, 34)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 34)-net in base 32, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 32m ≥ 1055 > 322 [i]
- m-reduction [i] would yield (0, 2, 34)-net in base 32, but