Best Known (22−7, 22, s)-Nets in Base 256
(22−7, 22, 2796457)-Net over F256 — Constructive and digital
Digital (15, 22, 2796457)-net over F256, using
- net defined by OOA [i] based on linear OOA(25622, 2796457, F256, 7, 7) (dual of [(2796457, 7), 19575177, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25622, 2796457, F256, 6, 7) (dual of [(2796457, 6), 16778720, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25622, 2796458, F256, 3, 7) (dual of [(2796458, 3), 8389352, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2563, 257, F256, 3, 3) (dual of [(257, 3), 768, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;768,256) [i]
- linear OOA(25619, 2796201, F256, 3, 7) (dual of [(2796201, 3), 8388584, 8]-NRT-code), using
- OOA 3-folding [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]
- OOA 3-folding [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- linear OOA(2563, 257, F256, 3, 3) (dual of [(257, 3), 768, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(25622, 2796458, F256, 3, 7) (dual of [(2796458, 3), 8389352, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25622, 2796457, F256, 6, 7) (dual of [(2796457, 6), 16778720, 8]-NRT-code), using
(22−7, 22, large)-Net over F256 — Digital
Digital (15, 22, large)-net over F256, using
- 2562 times duplication [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
(22−7, 22, large)-Net in Base 256 — Upper bound on s
There is no (15, 22, large)-net in base 256, because
- 5 times m-reduction [i] would yield (15, 17, large)-net in base 256, but