Best Known (42, 55, s)-Nets in Base 25
(42, 55, 65130)-Net over F25 — Constructive and digital
Digital (42, 55, 65130)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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, 49, 65104)-net over F25, using
- net defined by OOA [i] based on linear OOA(2549, 65104, F25, 13, 13) (dual of [(65104, 13), 846303, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using
- net defined by OOA [i] based on linear OOA(2549, 65104, F25, 13, 13) (dual of [(65104, 13), 846303, 14]-NRT-code), using
- digital (0, 6, 26)-net over F25, using
(42, 55, 562833)-Net over F25 — Digital
Digital (42, 55, 562833)-net over F25, using
(42, 55, large)-Net in Base 25 — Upper bound on s
There is no (42, 55, large)-net in base 25, because
- 11 times m-reduction [i] would yield (42, 44, large)-net in base 25, but