Best Known (13, 20, s)-Nets in Base 256
(13, 20, 2796200)-Net over F256 — Constructive and digital
Digital (13, 20, 2796200)-net over F256, using
- 2561 times duplication [i] based on digital (12, 19, 2796200)-net over F256, using
- net defined by OOA [i] based on linear OOA(25619, 2796200, F256, 7, 7) (dual of [(2796200, 7), 19573381, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25619, 2796200, F256, 6, 7) (dual of [(2796200, 6), 16777181, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(25619, 8388601, F256, 7) (dual of [8388601, 8388582, 8]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(25619, 8388601, F256, 7) (dual of [8388601, 8388582, 8]-code), using
- appending kth column [i] based on linear OOA(25619, 2796200, F256, 6, 7) (dual of [(2796200, 6), 16777181, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25619, 2796200, F256, 7, 7) (dual of [(2796200, 7), 19573381, 8]-NRT-code), using
(13, 20, large)-Net over F256 — Digital
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
(13, 20, large)-Net in Base 256 — Upper bound on s
There is no (13, 20, large)-net in base 256, because
- 5 times m-reduction [i] would yield (13, 15, large)-net in base 256, but