Best Known (83, 83+22, s)-Nets in Base 25
(83, 83+22, 35615)-Net over F25 — Constructive and digital
Digital (83, 105, 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 (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 (9, 20, 104)-net over F25, using
(83, 83+22, 3531691)-Net over F25 — Digital
Digital (83, 105, 3531691)-net over F25, using
(83, 83+22, large)-Net in Base 25 — Upper bound on s
There is no (83, 105, large)-net in base 25, because
- 20 times m-reduction [i] would yield (83, 85, large)-net in base 25, but