Best Known (25, 40, s)-Nets in Base 256
(25, 40, 9877)-Net over F256 — Constructive and digital
Digital (25, 40, 9877)-net over F256, using
- (u, u+v)-construction [i] based on
- 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
- net defined by OOA [i] based on linear OOA(25611, 515, F256, 7, 7) (dual of [(515, 7), 3594, 8]-NRT-code), using
- digital (14, 29, 9362)-net over F256, using
- net defined by OOA [i] based on linear OOA(25629, 9362, F256, 15, 15) (dual of [(9362, 15), 140401, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25629, 65535, F256, 15) (dual of [65535, 65506, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25629, 65535, F256, 15) (dual of [65535, 65506, 16]-code), using
- net defined by OOA [i] based on linear OOA(25629, 9362, F256, 15, 15) (dual of [(9362, 15), 140401, 16]-NRT-code), using
- digital (4, 11, 515)-net over F256, using
(25, 40, 180144)-Net over F256 — Digital
Digital (25, 40, 180144)-net over F256, using
(25, 40, large)-Net in Base 256 — Upper bound on s
There is no (25, 40, large)-net in base 256, because
- 13 times m-reduction [i] would yield (25, 27, large)-net in base 256, but