Best Known (82, 82+23, s)-Nets in Base 25
(82, 82+23, 35578)-Net over F25 — Constructive and digital
Digital (82, 105, 35578)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- 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
- digital (4, 15, 66)-net over F25, using
(82, 82+23, 1772682)-Net over F25 — Digital
Digital (82, 105, 1772682)-net over F25, using
(82, 82+23, large)-Net in Base 25 — Upper bound on s
There is no (82, 105, large)-net in base 25, because
- 21 times m-reduction [i] would yield (82, 84, large)-net in base 25, but