Best Known (52, 66, s)-Nets in Base 25
(52, 66, 1198371)-Net over F25 — Constructive and digital
Digital (52, 66, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
(52, 66, 8228581)-Net over F25 — Digital
Digital (52, 66, 8228581)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2566, 8228581, F25, 14) (dual of [8228581, 8228515, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
(52, 66, large)-Net in Base 25 — Upper bound on s
There is no (52, 66, large)-net in base 25, because
- 12 times m-reduction [i] would yield (52, 54, large)-net in base 25, but