Best Known (35, 35+3, s)-Nets in Base 25
(35, 35+3, large)-Net over F25 — Constructive and digital
Digital (35, 38, large)-net over F25, using
- 3 times m-reduction [i] based on digital (35, 41, large)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 391875)-net over F25, using
- s-reduction based on digital (0, 0, s)-net over F25 with arbitrarily large s, using
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 0, 391875)-net over F25 (see above)
- digital (0, 1, 391875)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 with arbitrarily large s, using
- digital (0, 1, 391875)-net over F25 (see above)
- digital (0, 1, 391875)-net over F25 (see above)
- digital (3, 5, 391875)-net over F25, using
- s-reduction based on digital (3, 5, 406901)-net over F25, using
- 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 (0, 0, 391875)-net over F25, using
- generalized (u, u+v)-construction [i] based on
(35, 35+3, large)-Net in Base 25 — Upper bound on s
There is no (35, 38, large)-net in base 25, because
- 1 times m-reduction [i] would yield (35, 37, large)-net in base 25, but