Best Known (86, 109, s)-Nets in Base 25
(86, 109, 35615)-Net over F25 — Constructive and digital
Digital (86, 109, 35615)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 20, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- 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 (9, 20, 104)-net over F25, using
(86, 109, 3182736)-Net over F25 — Digital
Digital (86, 109, 3182736)-net over F25, using
(86, 109, large)-Net in Base 25 — Upper bound on s
There is no (86, 109, large)-net in base 25, because
- 21 times m-reduction [i] would yield (86, 88, large)-net in base 25, but