Best Known (38−20, 38, s)-Nets in Base 256
(38−20, 38, 773)-Net over F256 — Constructive and digital
Digital (18, 38, 773)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 6, 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, 11, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (1, 21, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- digital (0, 6, 257)-net over F256, using
(38−20, 38, 2634)-Net over F256 — Digital
Digital (18, 38, 2634)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25638, 2634, F256, 20) (dual of [2634, 2596, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25638, 4369, F256, 20) (dual of [4369, 4331, 21]-code), using
(38−20, 38, large)-Net in Base 256 — Upper bound on s
There is no (18, 38, large)-net in base 256, because
- 18 times m-reduction [i] would yield (18, 20, large)-net in base 256, but