Best Known (85, 108, s)-Nets in Base 25
(85, 108, 35589)-Net over F25 — Constructive and digital
Digital (85, 108, 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 (66, 89, 35511)-net over F25, using
- net defined by OOA [i] based on linear OOA(2589, 35511, F25, 23, 23) (dual of [(35511, 23), 816664, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2589, 390622, F25, 23) (dual of [390622, 390533, 24]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2589, 390622, F25, 23) (dual of [390622, 390533, 24]-code), using
- net defined by OOA [i] based on linear OOA(2589, 35511, F25, 23, 23) (dual of [(35511, 23), 816664, 24]-NRT-code), using
- digital (8, 19, 78)-net over F25, using
(85, 108, 2749528)-Net over F25 — Digital
Digital (85, 108, 2749528)-net over F25, using
(85, 108, large)-Net in Base 25 — Upper bound on s
There is no (85, 108, large)-net in base 25, because
- 21 times m-reduction [i] would yield (85, 87, large)-net in base 25, but