Best Known (71, 71+25, s)-Nets in Base 25
(71, 71+25, 32551)-Net over F25 — Constructive and digital
Digital (71, 96, 32551)-net over F25, using
- net defined by OOA [i] based on linear OOA(2596, 32551, F25, 25, 25) (dual of [(32551, 25), 813679, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2596, 390613, F25, 25) (dual of [390613, 390517, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2596, 390624, F25, 25) (dual of [390624, 390528, 26]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2596, 390624, F25, 25) (dual of [390624, 390528, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2596, 390613, F25, 25) (dual of [390613, 390517, 26]-code), using
(71, 71+25, 233520)-Net over F25 — Digital
Digital (71, 96, 233520)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2596, 233520, F25, 25) (dual of [233520, 233424, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2596, 390624, F25, 25) (dual of [390624, 390528, 26]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2596, 390624, F25, 25) (dual of [390624, 390528, 26]-code), using
(71, 71+25, large)-Net in Base 25 — Upper bound on s
There is no (71, 96, large)-net in base 25, because
- 23 times m-reduction [i] would yield (71, 73, large)-net in base 25, but