Best Known (97−25, 97, s)-Nets in Base 25
(97−25, 97, 32552)-Net over F25 — Constructive and digital
Digital (72, 97, 32552)-net over F25, using
- net defined by OOA [i] based on linear OOA(2597, 32552, F25, 25, 25) (dual of [(32552, 25), 813703, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2597, 390625, F25, 25) (dual of [390625, 390528, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 390626, F25, 25) (dual of [390626, 390529, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2597, 390626, F25, 25) (dual of [390626, 390529, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2597, 390625, F25, 25) (dual of [390625, 390528, 26]-code), using
(97−25, 97, 268600)-Net over F25 — Digital
Digital (72, 97, 268600)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2597, 268600, F25, 25) (dual of [268600, 268503, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 390626, F25, 25) (dual of [390626, 390529, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2597, 390626, F25, 25) (dual of [390626, 390529, 26]-code), using
(97−25, 97, large)-Net in Base 25 — Upper bound on s
There is no (72, 97, large)-net in base 25, because
- 23 times m-reduction [i] would yield (72, 74, large)-net in base 25, but