Best Known (0, 57, s)-Nets in Base 32
(0, 57, 33)-Net over F32 — Constructive and digital
Digital (0, 57, 33)-net over F32, using
- net from sequence [i] based on 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, 57, 33)-Net in Base 32 — Upper bound on s
There is no (0, 57, 34)-net in base 32, because
- 55 times 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]