Best Known (47, 47+10, s)-Nets in Base 25
(47, 47+10, 1678621)-Net over F25 — Constructive and digital
Digital (47, 57, 1678621)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (6, 11, 901)-net over F25, using
- net defined by OOA [i] based on linear OOA(2511, 901, F25, 5, 5) (dual of [(901, 5), 4494, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2511, 1803, F25, 5) (dual of [1803, 1792, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(251, 601, F25, 1) (dual of [601, 600, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(253, 601, F25, 2) (dual of [601, 598, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using
- linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- linear OA(251, 601, F25, 1) (dual of [601, 600, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(2511, 1803, F25, 5) (dual of [1803, 1792, 6]-code), using
- net defined by OOA [i] based on linear OOA(2511, 901, F25, 5, 5) (dual of [(901, 5), 4494, 6]-NRT-code), using
- 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 (6, 11, 901)-net over F25, using
(47, 47+10, large)-Net over F25 — Digital
Digital (47, 57, large)-net over F25, using
- 251 times duplication [i] based on digital (46, 56, large)-net over F25, using
- t-expansion [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
- t-expansion [i] based on digital (44, 56, large)-net over F25, using
(47, 47+10, large)-Net in Base 25 — Upper bound on s
There is no (47, 57, large)-net in base 25, because
- 8 times m-reduction [i] would yield (47, 49, large)-net in base 25, but