Best Known (69, 69+23, s)-Nets in Base 25
(69, 69+23, 35513)-Net over F25 — Constructive and digital
Digital (69, 92, 35513)-net over F25, using
- net defined by OOA [i] based on linear OOA(2592, 35513, F25, 23, 23) (dual of [(35513, 23), 816707, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2592, 390644, F25, 23) (dual of [390644, 390552, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2592, 390645, F25, 23) (dual of [390645, 390553, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- 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(2573, 390626, F25, 19) (dual of [390626, 390553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2592, 390645, F25, 23) (dual of [390645, 390553, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2592, 390644, F25, 23) (dual of [390644, 390552, 24]-code), using
(69, 69+23, 390645)-Net over F25 — Digital
Digital (69, 92, 390645)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2592, 390645, F25, 23) (dual of [390645, 390553, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- 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(2573, 390626, F25, 19) (dual of [390626, 390553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
(69, 69+23, large)-Net in Base 25 — Upper bound on s
There is no (69, 92, large)-net in base 25, because
- 21 times m-reduction [i] would yield (69, 71, large)-net in base 25, but