Best Known (38, 52, s)-Nets in Base 256
(38, 52, 1199142)-Net over F256 — Constructive and digital
Digital (38, 52, 1199142)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (5, 12, 771)-net over F256, using
- net defined by OOA [i] based on linear OOA(25612, 771, F256, 7, 7) (dual of [(771, 7), 5385, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25612, 771, F256, 6, 7) (dual of [(771, 6), 4614, 8]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(2562, 257, F256, 6, 2) (dual of [(257, 6), 1540, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1540,256) [i]
- 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(2567, 257, F256, 6, 7) (dual of [(257, 6), 1535, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1535,256) [i]
- linear OOA(2562, 257, F256, 6, 2) (dual of [(257, 6), 1540, 3]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(25612, 771, F256, 6, 7) (dual of [(771, 6), 4614, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25612, 771, F256, 7, 7) (dual of [(771, 7), 5385, 8]-NRT-code), using
- digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- digital (5, 12, 771)-net over F256, using
(38, 52, large)-Net over F256 — Digital
Digital (38, 52, large)-net over F256, using
- 3 times m-reduction [i] based on digital (38, 55, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25655, large, F256, 17) (dual of [large, large−55, 18]-code), using
- strength reduction [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- strength reduction [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25655, large, F256, 17) (dual of [large, large−55, 18]-code), using
(38, 52, large)-Net in Base 256 — Upper bound on s
There is no (38, 52, large)-net in base 256, because
- 12 times m-reduction [i] would yield (38, 40, large)-net in base 256, but