Best Known (45, 57, s)-Nets in Base 25
(45, 57, 1398100)-Net over F25 — Constructive and digital
Digital (45, 57, 1398100)-net over F25, using
- 251 times duplication [i] based on digital (44, 56, 1398100)-net over F25, using
- net defined by OOA [i] based on linear OOA(2556, 1398100, F25, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2556, 8388600, F25, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2556, 8388600, F25, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(2556, 1398100, F25, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
(45, 57, large)-Net over F25 — Digital
Digital (45, 57, large)-net over F25, using
- 251 times duplication [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
(45, 57, large)-Net in Base 25 — Upper bound on s
There is no (45, 57, large)-net in base 25, because
- 10 times m-reduction [i] would yield (45, 47, large)-net in base 25, but