Best Known (46−13, 46, s)-Nets in Base 256
(46−13, 46, 1398614)-Net over F256 — Constructive and digital
Digital (33, 46, 1398614)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 514)-net over F256, using
- net defined by OOA [i] based on linear OOA(2569, 514, F256, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2569, 514, F256, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2563, 257, F256, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;1282,256) [i]
- linear OOA(2566, 257, F256, 5, 6) (dual of [(257, 5), 1279, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;1279,256) [i]
- linear OOA(2563, 257, F256, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2569, 514, F256, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2569, 514, F256, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), using
- digital (24, 37, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- digital (3, 9, 514)-net over F256, using
(46−13, 46, large)-Net over F256 — Digital
Digital (33, 46, large)-net over F256, using
- 2 times m-reduction [i] based on digital (33, 48, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25648, large, F256, 15) (dual of [large, large−48, 16]-code), using
- 5 times code embedding in larger space [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 5 times code embedding in larger space [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25648, large, F256, 15) (dual of [large, large−48, 16]-code), using
(46−13, 46, large)-Net in Base 256 — Upper bound on s
There is no (33, 46, large)-net in base 256, because
- 11 times m-reduction [i] would yield (33, 35, large)-net in base 256, but