Best Known (26−6, 26, s)-Nets in Base 25
(26−6, 26, 2796201)-Net over F25 — Constructive and digital
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
(26−6, 26, large)-Net over F25 — Digital
Digital (20, 26, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [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]
(26−6, 26, large)-Net in Base 25 — Upper bound on s
There is no (20, 26, large)-net in base 25, because
- 4 times m-reduction [i] would yield (20, 22, large)-net in base 25, but