Best Known (32−17, 32, s)-Nets in Base 256
(32−17, 32, 773)-Net over F256 — Constructive and digital
Digital (15, 32, 773)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 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]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (1, 9, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- digital (0, 5, 257)-net over F256, using
(32−17, 32, 2383)-Net over F256 — Digital
Digital (15, 32, 2383)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25632, 2383, F256, 17) (dual of [2383, 2351, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(25632, 3855, F256, 17) (dual of [3855, 3823, 18]-code), using
(32−17, 32, large)-Net in Base 256 — Upper bound on s
There is no (15, 32, large)-net in base 256, because
- 15 times m-reduction [i] would yield (15, 17, large)-net in base 256, but