Best Known (42, 42+10, s)-Nets in Base 25
(42, 42+10, 1677747)-Net over F25 — Constructive and digital
Digital (42, 52, 1677747)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, 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 (1, 6, 27)-net over F25, using
(42, 42+10, large)-Net over F25 — Digital
Digital (42, 52, large)-net over F25, using
- 251 times duplication [i] based on digital (41, 51, large)-net over F25, using
- t-expansion [i] based on digital (40, 51, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- t-expansion [i] based on digital (40, 51, large)-net over F25, using
(42, 42+10, large)-Net in Base 25 — Upper bound on s
There is no (42, 52, large)-net in base 25, because
- 8 times m-reduction [i] would yield (42, 44, large)-net in base 25, but