Best Known (82, 82+26, s)-Nets in Base 25
(82, 82+26, 30051)-Net over F25 — Constructive and digital
Digital (82, 108, 30051)-net over F25, using
- 251 times duplication [i] based on digital (81, 107, 30051)-net over F25, using
- net defined by OOA [i] based on linear OOA(25107, 30051, F25, 26, 26) (dual of [(30051, 26), 781219, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25107, 390663, F25, 26) (dual of [390663, 390556, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2569, 390625, F25, 18) (dual of [390625, 390556, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2510, 38, F25, 7) (dual of [38, 28, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2510, 49, F25, 7) (dual of [49, 39, 8]-code), using
- an extension Ce(6) of the narrow-sense BCH-code C(I) with length 48 | 252−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(2510, 49, F25, 7) (dual of [49, 39, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- OA 13-folding and stacking [i] based on linear OA(25107, 390663, F25, 26) (dual of [390663, 390556, 27]-code), using
- net defined by OOA [i] based on linear OOA(25107, 30051, F25, 26, 26) (dual of [(30051, 26), 781219, 27]-NRT-code), using
(82, 82+26, 464010)-Net over F25 — Digital
Digital (82, 108, 464010)-net over F25, using
(82, 82+26, large)-Net in Base 25 — Upper bound on s
There is no (82, 108, large)-net in base 25, because
- 24 times m-reduction [i] would yield (82, 84, large)-net in base 25, but