Best Known (70, 93, s)-Nets in Base 25
(70, 93, 35513)-Net over F25 — Constructive and digital
Digital (70, 93, 35513)-net over F25, using
- 251 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(2592, 35513, F25, 23, 23) (dual of [(35513, 23), 816707, 24]-NRT-code), using
(70, 93, 390649)-Net over F25 — Digital
Digital (70, 93, 390649)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2593, 390649, F25, 23) (dual of [390649, 390556, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2569, 390625, F25, 18) (dual of [390625, 390556, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
(70, 93, large)-Net in Base 25 — Upper bound on s
There is no (70, 93, large)-net in base 25, because
- 21 times m-reduction [i] would yield (70, 72, large)-net in base 25, but