Best Known (33, 33+6, s)-Nets in Base 25
(33, 33+6, 5608678)-Net over F25 — Constructive and digital
Digital (33, 39, 5608678)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 4, 16276)-net over F25, using
- digital (6, 9, 2796201)-net over F25, using
- s-reduction based on digital (6, 9, large)-net over F25, using
- net defined by OOA [i] based on linear OOA(259, large, F25, 3, 3), using
- appending kth column [i] based on linear OOA(259, large, F25, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(259, large, F25, 3) (dual of [large, large−9, 4]-code), using
- appending kth column [i] based on linear OOA(259, large, F25, 2, 3), using
- net defined by OOA [i] based on linear OOA(259, large, F25, 3, 3), using
- s-reduction based on digital (6, 9, large)-net over F25, 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
(33, 33+6, large)-Net over F25 — Digital
Digital (33, 39, large)-net over F25, using
- t-expansion [i] based on digital (32, 39, large)-net over F25, using
- 2 times m-reduction [i] based on digital (32, 41, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- 2 times m-reduction [i] based on digital (32, 41, large)-net over F25, using
(33, 33+6, large)-Net in Base 25 — Upper bound on s
There is no (33, 39, large)-net in base 25, because
- 4 times m-reduction [i] would yield (33, 35, large)-net in base 25, but