Best Known (35, 46, s)-Nets in Base 25
(35, 46, 78151)-Net over F25 — Constructive and digital
Digital (35, 46, 78151)-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 (30, 41, 78125)-net over F25, using
- net defined by OOA [i] based on linear OOA(2541, 78125, F25, 11, 11) (dual of [(78125, 11), 859334, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2541, 390626, F25, 11) (dual of [390626, 390585, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(2541, 390626, F25, 11) (dual of [390626, 390585, 12]-code), using
- net defined by OOA [i] based on linear OOA(2541, 78125, F25, 11, 11) (dual of [(78125, 11), 859334, 12]-NRT-code), using
- digital (0, 5, 26)-net over F25, using
(35, 46, 508503)-Net over F25 — Digital
Digital (35, 46, 508503)-net over F25, using
(35, 46, large)-Net in Base 25 — Upper bound on s
There is no (35, 46, large)-net in base 25, because
- 9 times m-reduction [i] would yield (35, 37, large)-net in base 25, but