Best Known (13, 13+6, s)-Nets in Base 256
(13, 13+6, 2796458)-Net over F256 — Constructive and digital
Digital (13, 19, 2796458)-net over F256, using
- net defined by OOA [i] based on linear OOA(25619, 2796458, F256, 6, 6) (dual of [(2796458, 6), 16778729, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(25619, 2796458, F256, 5, 6) (dual of [(2796458, 5), 13982271, 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(25616, 2796201, F256, 5, 6) (dual of [(2796201, 5), 13980989, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- 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(25619, 2796458, F256, 5, 6) (dual of [(2796458, 5), 13982271, 7]-NRT-code), using
(13, 13+6, large)-Net over F256 — Digital
Digital (13, 19, large)-net over F256, using
- 1 times m-reduction [i] based on digital (13, 20, large)-net over F256, using
- net defined by OOA [i] based on linear OOA(25620, large, F256, 7, 7), using
- appending kth column [i] based on linear OOA(25620, large, F256, 6, 7), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25620, large, F256, 7) (dual of [large, large−20, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 1 times code embedding in larger space [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25620, large, F256, 7) (dual of [large, large−20, 8]-code), using
- appending kth column [i] based on linear OOA(25620, large, F256, 6, 7), using
- net defined by OOA [i] based on linear OOA(25620, large, F256, 7, 7), using
(13, 13+6, large)-Net in Base 256 — Upper bound on s
There is no (13, 19, large)-net in base 256, because
- 4 times m-reduction [i] would yield (13, 15, large)-net in base 256, but