Best Known (11−7, 11, s)-Nets in Base 256
(11−7, 11, 515)-Net over F256 — Constructive and digital
Digital (4, 11, 515)-net over F256, using
- net defined by OOA [i] based on linear OOA(25611, 515, F256, 7, 7) (dual of [(515, 7), 3594, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25611, 515, F256, 6, 7) (dual of [(515, 6), 3079, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2563, 257, F256, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1539,256) [i]
- linear OOA(2568, 258, F256, 6, 7) (dual of [(258, 6), 1540, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 8, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- extracting embedded OOA [i] based on digital (1, 8, 258)-net over F256, using
- linear OOA(2563, 257, F256, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(25611, 515, F256, 6, 7) (dual of [(515, 6), 3079, 8]-NRT-code), using
(11−7, 11, 668)-Net over F256 — Digital
Digital (4, 11, 668)-net over F256, using
- net defined by OOA [i] based on linear OOA(25611, 668, F256, 7, 7) (dual of [(668, 7), 4665, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25611, 668, F256, 6, 7) (dual of [(668, 6), 3997, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25611, 668, F256, 7) (dual of [668, 657, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(25611, 771, F256, 7) (dual of [771, 760, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25611, 668, F256, 7) (dual of [668, 657, 8]-code), using
- appending kth column [i] based on linear OOA(25611, 668, F256, 6, 7) (dual of [(668, 6), 3997, 8]-NRT-code), using
(11−7, 11, 759118)-Net in Base 256 — Upper bound on s
There is no (4, 11, 759119)-net in base 256, because
- 1 times m-reduction [i] would yield (4, 10, 759119)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 1 208928 488788 191571 534036 > 25610 [i]