Best Known (34−6, 34, s)-Nets in Base 25
(34−6, 34, 3754952)-Net over F25 — Constructive and digital
Digital (28, 34, 3754952)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (5, 8, 958751)-net over F25, using
- net defined by OOA [i] based on linear OOA(258, 958751, F25, 3, 3) (dual of [(958751, 3), 2876245, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(258, 958751, F25, 2, 3) (dual of [(958751, 2), 1917494, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(258, 958751, F25, 3) (dual of [958751, 958743, 4]-code or 958751-cap in PG(7,25)), using
- appending kth column [i] based on linear OOA(258, 958751, F25, 2, 3) (dual of [(958751, 2), 1917494, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(258, 958751, F25, 3, 3) (dual of [(958751, 3), 2876245, 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 (5, 8, 958751)-net over F25, using
(34−6, 34, large)-Net over F25 — Digital
Digital (28, 34, large)-net over F25, using
- 2 times m-reduction [i] based on digital (28, 36, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
(34−6, 34, large)-Net in Base 25 — Upper bound on s
There is no (28, 34, large)-net in base 25, because
- 4 times m-reduction [i] would yield (28, 30, large)-net in base 25, but