Best Known (73−17, 73, s)-Nets in Base 25
(73−17, 73, 48854)-Net over F25 — Constructive and digital
Digital (56, 73, 48854)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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 (48, 65, 48828)-net over F25, using
- net defined by OOA [i] based on linear OOA(2565, 48828, F25, 17, 17) (dual of [(48828, 17), 830011, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using
- net defined by OOA [i] based on linear OOA(2565, 48828, F25, 17, 17) (dual of [(48828, 17), 830011, 18]-NRT-code), using
- digital (0, 8, 26)-net over F25, using
(73−17, 73, 676759)-Net over F25 — Digital
Digital (56, 73, 676759)-net over F25, using
(73−17, 73, large)-Net in Base 25 — Upper bound on s
There is no (56, 73, large)-net in base 25, because
- 15 times m-reduction [i] would yield (56, 58, large)-net in base 25, but