Best Known (59−20, 59, s)-Nets in Base 256
(59−20, 59, 838860)-Net over F256 — Constructive and digital
Digital (39, 59, 838860)-net over F256, using
- 2561 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(25658, 838860, F256, 20, 20) (dual of [(838860, 20), 16777142, 21]-NRT-code), using
(59−20, 59, 3342651)-Net over F256 — Digital
Digital (39, 59, 3342651)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25659, 3342651, F256, 2, 20) (dual of [(3342651, 2), 6685243, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25659, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388543, 21]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 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
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- 2561 times duplication [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25659, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388543, 21]-NRT-code), using
(59−20, 59, large)-Net in Base 256 — Upper bound on s
There is no (39, 59, large)-net in base 256, because
- 18 times m-reduction [i] would yield (39, 41, large)-net in base 256, but