Best Known (59, 73, s)-Nets in Base 25
(59, 73, 1198397)-Net over F25 — Constructive and digital
Digital (59, 73, 1198397)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (52, 66, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (0, 7, 26)-net over F25, using
(59, 73, large)-Net over F25 — Digital
Digital (59, 73, large)-net over F25, using
- 251 times duplication [i] based on digital (58, 72, large)-net over F25, using
- t-expansion [i] based on digital (57, 72, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2572, large, F25, 15) (dual of [large, large−72, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2572, large, F25, 15) (dual of [large, large−72, 16]-code), using
- t-expansion [i] based on digital (57, 72, large)-net over F25, using
(59, 73, large)-Net in Base 25 — Upper bound on s
There is no (59, 73, large)-net in base 25, because
- 12 times m-reduction [i] would yield (59, 61, large)-net in base 25, but