Best Known (61−21, 61, s)-Nets in Base 256
(61−21, 61, 838860)-Net over F256 — Constructive and digital
Digital (40, 61, 838860)-net over F256, using
- net defined by OOA [i] based on linear OOA(25661, 838860, F256, 21, 21) (dual of [(838860, 21), 17615999, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25661, 8388601, F256, 21) (dual of [8388601, 8388540, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25661, 8388601, F256, 21) (dual of [8388601, 8388540, 22]-code), using
(61−21, 61, 2796201)-Net over F256 — Digital
Digital (40, 61, 2796201)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25661, 2796201, F256, 3, 21) (dual of [(2796201, 3), 8388542, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- OOA 3-folding [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
(61−21, 61, large)-Net in Base 256 — Upper bound on s
There is no (40, 61, large)-net in base 256, because
- 19 times m-reduction [i] would yield (40, 42, large)-net in base 256, but