Best Known (42−42, 42, s)-Nets in Base 256
(42−42, 42, 257)-Net over F256 — Constructive and digital
Digital (0, 42, 257)-net over F256, using
- net from sequence [i] based on 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]
(42−42, 42, 257)-Net in Base 256 — Upper bound on s
There is no (0, 42, 258)-net in base 256, because
- 40 times 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]