Best Known (71, 71+26, s)-Nets in Base 25
(71, 71+26, 30048)-Net over F25 — Constructive and digital
Digital (71, 97, 30048)-net over F25, using
- net defined by OOA [i] based on linear OOA(2597, 30048, F25, 26, 26) (dual of [(30048, 26), 781151, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2597, 390624, F25, 26) (dual of [390624, 390527, 27]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2597, 390624, F25, 26) (dual of [390624, 390527, 27]-code), using
(71, 71+26, 195312)-Net over F25 — Digital
Digital (71, 97, 195312)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2597, 195312, F25, 2, 26) (dual of [(195312, 2), 390527, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2597, 390624, F25, 26) (dual of [390624, 390527, 27]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using
- OOA 2-folding [i] based on linear OA(2597, 390624, F25, 26) (dual of [390624, 390527, 27]-code), using
(71, 71+26, large)-Net in Base 25 — Upper bound on s
There is no (71, 97, large)-net in base 25, because
- 24 times m-reduction [i] would yield (71, 73, large)-net in base 25, but