Best Known (13−8, 13, s)-Nets in Base 256
(13−8, 13, 515)-Net over F256 — Constructive and digital
Digital (5, 13, 515)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (0, 4, 257)-net over F256, using
(13−8, 13, 767)-Net over F256 — Digital
Digital (5, 13, 767)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25613, 767, F256, 8) (dual of [767, 754, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25613, 771, F256, 8) (dual of [771, 758, 9]-code), using
(13−8, 13, 582493)-Net in Base 256 — Upper bound on s
There is no (5, 13, 582494)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 20 282422 504132 163617 165016 448631 > 25613 [i]