Best Known (41, 62, s)-Nets in Base 256
(41, 62, 838860)-Net over F256 — Constructive and digital
Digital (41, 62, 838860)-net over F256, using
- 2561 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(25661, 838860, F256, 21, 21) (dual of [(838860, 21), 17615999, 22]-NRT-code), using
(41, 62, 3155407)-Net over F256 — Digital
Digital (41, 62, 3155407)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25662, 3155407, F256, 2, 21) (dual of [(3155407, 2), 6310752, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25662, 4194301, F256, 2, 21) (dual of [(4194301, 2), 8388540, 22]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25661, 4194301, F256, 2, 21) (dual of [(4194301, 2), 8388541, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25661, 8388602, F256, 21) (dual of [8388602, 8388541, 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 2-folding [i] based on linear OA(25661, 8388602, F256, 21) (dual of [8388602, 8388541, 22]-code), using
- 2561 times duplication [i] based on linear OOA(25661, 4194301, F256, 2, 21) (dual of [(4194301, 2), 8388541, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25662, 4194301, F256, 2, 21) (dual of [(4194301, 2), 8388540, 22]-NRT-code), using
(41, 62, large)-Net in Base 256 — Upper bound on s
There is no (41, 62, large)-net in base 256, because
- 19 times m-reduction [i] would yield (41, 43, large)-net in base 256, but