Best Known (58−20, 58, s)-Nets in Base 256
(58−20, 58, 838860)-Net over F256 — Constructive and digital
Digital (38, 58, 838860)-net over F256, using
- net defined by OOA [i] based on linear OOA(25658, 838860, F256, 20, 20) (dual of [(838860, 20), 16777142, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25658, 8388600, F256, 20) (dual of [8388600, 8388542, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(25658, 8388600, F256, 20) (dual of [8388600, 8388542, 21]-code), using
(58−20, 58, 2796201)-Net over F256 — Digital
Digital (38, 58, 2796201)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25658, 2796201, F256, 3, 20) (dual of [(2796201, 3), 8388545, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 3-folding [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
(58−20, 58, large)-Net in Base 256 — Upper bound on s
There is no (38, 58, large)-net in base 256, because
- 18 times m-reduction [i] would yield (38, 40, large)-net in base 256, but