Best Known (37, 45, s)-Nets in Base 25
(37, 45, 2098126)-Net over F25 — Constructive and digital
Digital (37, 45, 2098126)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (5, 9, 976)-net over F25, using
- net defined by OOA [i] based on linear OOA(259, 976, F25, 4, 4) (dual of [(976, 4), 3895, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(259, 1952, F25, 4) (dual of [1952, 1943, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(259, 1953, F25, 4) (dual of [1953, 1944, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(259, 1952, F25, 4) (dual of [1952, 1943, 5]-code), using
- net defined by OOA [i] based on linear OOA(259, 976, F25, 4, 4) (dual of [(976, 4), 3895, 5]-NRT-code), using
- digital (28, 36, 2097150)-net over F25, using
- net defined by OOA [i] based on linear OOA(2536, 2097150, F25, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2536, 8388600, F25, 8) (dual of [8388600, 8388564, 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
- OA 4-folding and stacking [i] based on linear OA(2536, 8388600, F25, 8) (dual of [8388600, 8388564, 9]-code), using
- net defined by OOA [i] based on linear OOA(2536, 2097150, F25, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- digital (5, 9, 976)-net over F25, using
(37, 45, large)-Net over F25 — Digital
Digital (37, 45, large)-net over F25, using
- t-expansion [i] based on digital (36, 45, large)-net over F25, using
- 1 times m-reduction [i] based on digital (36, 46, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] 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]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- 1 times m-reduction [i] based on digital (36, 46, large)-net over F25, using
(37, 45, large)-Net in Base 25 — Upper bound on s
There is no (37, 45, large)-net in base 25, because
- 6 times m-reduction [i] would yield (37, 39, large)-net in base 25, but