Best Known (44, 44+8, s)-Nets in Base 25
(44, 44+8, 4194300)-Net over F25 — Constructive and digital
Digital (44, 52, 4194300)-net over F25, using
- net defined by OOA [i] based on linear OOA(2552, 4194300, F25, 10, 8) (dual of [(4194300, 10), 41942948, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2552, 8388601, F25, 2, 8) (dual of [(8388601, 2), 16777150, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2552, 8388602, F25, 2, 8) (dual of [(8388602, 2), 16777152, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2516, 4194301, F25, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- OOA 2-folding [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- linear OOA(2536, 4194301, F25, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- linear OOA(2516, 4194301, F25, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2552, 8388602, F25, 2, 8) (dual of [(8388602, 2), 16777152, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2552, 8388601, F25, 2, 8) (dual of [(8388601, 2), 16777150, 9]-NRT-code), using
(44, 44+8, large)-Net over F25 — Digital
Digital (44, 52, large)-net over F25, using
- 4 times m-reduction [i] based on digital (44, 56, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
(44, 44+8, large)-Net in Base 25 — Upper bound on s
There is no (44, 52, large)-net in base 25, because
- 6 times m-reduction [i] would yield (44, 46, large)-net in base 25, but