Best Known (78−78, 78, s)-Nets in Base 32
(78−78, 78, 33)-Net over F32 — Constructive and digital
Digital (0, 78, 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]
(78−78, 78, 33)-Net in Base 32 — Upper bound on s
There is no (0, 78, 34)-net in base 32, because
- 76 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]