Best Known (19, 19+21, s)-Nets in Base 256
(19, 19+21, 773)-Net over F256 — Constructive and digital
Digital (19, 40, 773)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 7, 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, 22, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- digital (0, 7, 257)-net over F256, using
(19, 19+21, 2720)-Net over F256 — Digital
Digital (19, 40, 2720)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25640, 2720, F256, 21) (dual of [2720, 2680, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, 4369, F256, 21) (dual of [4369, 4329, 22]-code), using
(19, 19+21, large)-Net in Base 256 — Upper bound on s
There is no (19, 40, large)-net in base 256, because
- 19 times m-reduction [i] would yield (19, 21, large)-net in base 256, but