Best Known (37, 51, s)-Nets in Base 256
(37, 51, 1198886)-Net over F256 — Constructive and digital
Digital (37, 51, 1198886)-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 (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 (4, 11, 515)-net over F256, using
(37, 51, large)-Net over F256 — Digital
Digital (37, 51, large)-net over F256, using
- t-expansion [i] based on digital (35, 51, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25651, large, F256, 16) (dual of [large, large−51, 17]-code), using
- 5 times code embedding in larger space [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 5 times code embedding in larger space [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25651, large, F256, 16) (dual of [large, large−51, 17]-code), using
(37, 51, large)-Net in Base 256 — Upper bound on s
There is no (37, 51, large)-net in base 256, because
- 12 times m-reduction [i] would yield (37, 39, large)-net in base 256, but