Best Known (47−11, 47, s)-Nets in Base 25
(47−11, 47, 78152)-Net over F25 — Constructive and digital
Digital (36, 47, 78152)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-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 (1, 6, 27)-net over F25, using
(47−11, 47, 701594)-Net over F25 — Digital
Digital (36, 47, 701594)-net over F25, using
(47−11, 47, large)-Net in Base 25 — Upper bound on s
There is no (36, 47, large)-net in base 25, because
- 9 times m-reduction [i] would yield (36, 38, large)-net in base 25, but