Best Known (51, 51+10, s)-Nets in Base 25
(51, 51+10, 1685870)-Net over F25 — Constructive and digital
Digital (51, 61, 1685870)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 15, 8150)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 326)-net over F25, using
- s-reduction based on digital (0, 0, s)-net over F25 with arbitrarily large s, using
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 0, 326)-net over F25 (see above)
- digital (0, 1, 326)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 with arbitrarily large s, using
- digital (0, 1, 326)-net over F25 (see above)
- digital (0, 1, 326)-net over F25 (see above)
- digital (1, 3, 326)-net over F25, using
- s-reduction based on digital (1, 3, 651)-net over F25, using
- digital (4, 9, 326)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 26)-net over F25, using
- digital (2, 7, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- digital (0, 0, 326)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (36, 46, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- digital (10, 15, 8150)-net over F25, using
(51, 51+10, large)-Net over F25 — Digital
Digital (51, 61, large)-net over F25, using
- t-expansion [i] based on digital (48, 61, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
(51, 51+10, large)-Net in Base 25 — Upper bound on s
There is no (51, 61, large)-net in base 25, because
- 8 times m-reduction [i] would yield (51, 53, large)-net in base 25, but