Best Known (27, 27+6, s)-Nets in Base 25
(27, 27+6, 3188076)-Net over F25 — Constructive and digital
Digital (27, 33, 3188076)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 7, 391875)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 391875, F25, 3, 3) (dual of [(391875, 3), 1175618, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(257, 391875, F25, 2, 3) (dual of [(391875, 2), 783743, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(257, 391875, F25, 3, 3) (dual of [(391875, 3), 1175618, 4]-NRT-code), using
- digital (20, 26, 2796201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- digital (4, 7, 391875)-net over F25, using
(27, 27+6, large)-Net over F25 — Digital
Digital (27, 33, large)-net over F25, using
- 252 times duplication [i] based on digital (25, 31, large)-net over F25, using
- t-expansion [i] based on digital (24, 31, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2531, large, F25, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2531, large, F25, 7) (dual of [large, large−31, 8]-code), using
- t-expansion [i] based on digital (24, 31, large)-net over F25, using
(27, 27+6, large)-Net in Base 25 — Upper bound on s
There is no (27, 33, large)-net in base 25, because
- 4 times m-reduction [i] would yield (27, 29, large)-net in base 25, but