Best Known (40−14, 40, s)-Nets in Base 256
(40−14, 40, 1198371)-Net over F256 — Constructive and digital
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
(40−14, 40, 4016501)-Net over F256 — Digital
Digital (26, 40, 4016501)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25640, 4016501, F256, 2, 14) (dual of [(4016501, 2), 8032962, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25640, 4194301, F256, 2, 14) (dual of [(4194301, 2), 8388562, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25640, 8388602, F256, 14) (dual of [8388602, 8388562, 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
- OOA 2-folding [i] based on linear OA(25640, 8388602, F256, 14) (dual of [8388602, 8388562, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(25640, 4194301, F256, 2, 14) (dual of [(4194301, 2), 8388562, 15]-NRT-code), using
(40−14, 40, large)-Net in Base 256 — Upper bound on s
There is no (26, 40, large)-net in base 256, because
- 12 times m-reduction [i] would yield (26, 28, large)-net in base 256, but