Best Known (45, 45+19, s)-Nets in Base 25
(45, 45+19, 1762)-Net over F25 — Constructive and digital
Digital (45, 64, 1762)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (36, 55, 1736)-net over F25, using
- net defined by OOA [i] based on linear OOA(2555, 1736, F25, 19, 19) (dual of [(1736, 19), 32929, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using
- net defined by OOA [i] based on linear OOA(2555, 1736, F25, 19, 19) (dual of [(1736, 19), 32929, 20]-NRT-code), using
- digital (0, 9, 26)-net over F25, using
(45, 45+19, 29411)-Net over F25 — Digital
Digital (45, 64, 29411)-net over F25, using
(45, 45+19, large)-Net in Base 25 — Upper bound on s
There is no (45, 64, large)-net in base 25, because
- 17 times m-reduction [i] would yield (45, 47, large)-net in base 25, but