Best Known (91−23, 91, s)-Nets in Base 25
(91−23, 91, 35512)-Net over F25 — Constructive and digital
Digital (68, 91, 35512)-net over F25, using
- 251 times duplication [i] based on digital (67, 90, 35512)-net over F25, using
- net defined by OOA [i] based on linear OOA(2590, 35512, F25, 23, 23) (dual of [(35512, 23), 816686, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2590, 390633, F25, 23) (dual of [390633, 390543, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2590, 390635, F25, 23) (dual of [390635, 390545, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [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(2581, 390626, F25, 21) (dual of [390626, 390545, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,11]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2590, 390635, F25, 23) (dual of [390635, 390545, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2590, 390633, F25, 23) (dual of [390633, 390543, 24]-code), using
- net defined by OOA [i] based on linear OOA(2590, 35512, F25, 23, 23) (dual of [(35512, 23), 816686, 24]-NRT-code), using
(91−23, 91, 354356)-Net over F25 — Digital
Digital (68, 91, 354356)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2591, 354356, F25, 23) (dual of [354356, 354265, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2591, 390639, F25, 23) (dual of [390639, 390548, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [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(2577, 390625, F25, 20) (dual of [390625, 390548, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(252, 14, F25, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2591, 390639, F25, 23) (dual of [390639, 390548, 24]-code), using
(91−23, 91, large)-Net in Base 25 — Upper bound on s
There is no (68, 91, large)-net in base 25, because
- 21 times m-reduction [i] would yield (68, 70, large)-net in base 25, but