Best Known (61−20, 61, s)-Nets in Base 256
(61−20, 61, 838860)-Net over F256 — Constructive and digital
Digital (41, 61, 838860)-net over F256, using
- t-expansion [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
(61−20, 61, 4194302)-Net over F256 — Digital
Digital (41, 61, 4194302)-net over F256, using
- 2561 times duplication [i] based on digital (40, 60, 4194302)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25660, 4194302, F256, 2, 20) (dual of [(4194302, 2), 8388544, 21]-NRT-code), using
- 1 times NRT-code embedding in larger space [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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25660, 4194302, F256, 2, 20) (dual of [(4194302, 2), 8388544, 21]-NRT-code), using
(61−20, 61, large)-Net in Base 256 — Upper bound on s
There is no (41, 61, large)-net in base 256, because
- 18 times m-reduction [i] would yield (41, 43, large)-net in base 256, but