Best Known (73, 73+25, s)-Nets in Base 25
(73, 73+25, 32552)-Net over F25 — Constructive and digital
Digital (73, 98, 32552)-net over F25, using
- 251 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(2597, 32552, F25, 25, 25) (dual of [(32552, 25), 813703, 26]-NRT-code), using
(73, 73+25, 308951)-Net over F25 — Digital
Digital (73, 98, 308951)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2598, 308951, F25, 25) (dual of [308951, 308853, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2598, 390635, F25, 25) (dual of [390635, 390537, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] 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]
- linear OA(2589, 390626, F25, 23) (dual of [390626, 390537, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2598, 390635, F25, 25) (dual of [390635, 390537, 26]-code), using
(73, 73+25, large)-Net in Base 25 — Upper bound on s
There is no (73, 98, large)-net in base 25, because
- 23 times m-reduction [i] would yield (73, 75, large)-net in base 25, but