Best Known (82, 104, s)-Nets in Base 25
(82, 104, 35589)-Net over F25 — Constructive and digital
Digital (82, 104, 35589)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (8, 19, 78)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (3, 14, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (0, 5, 26)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (63, 85, 35511)-net over F25, using
- net defined by OOA [i] based on linear OOA(2585, 35511, F25, 22, 22) (dual of [(35511, 22), 781157, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2585, 390621, F25, 22) (dual of [390621, 390536, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2585, 390621, F25, 22) (dual of [390621, 390536, 23]-code), using
- net defined by OOA [i] based on linear OOA(2585, 35511, F25, 22, 22) (dual of [(35511, 22), 781157, 23]-NRT-code), using
- digital (8, 19, 78)-net over F25, using
(82, 104, 3029802)-Net over F25 — Digital
Digital (82, 104, 3029802)-net over F25, using
(82, 104, large)-Net in Base 25 — Upper bound on s
There is no (82, 104, large)-net in base 25, because
- 20 times m-reduction [i] would yield (82, 84, large)-net in base 25, but