Best Known (81, 81+24, s)-Nets in Base 25
(81, 81+24, 32578)-Net over F25 — Constructive and digital
Digital (81, 105, 32578)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 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 (69, 93, 32552)-net over F25, using
- net defined by OOA [i] based on linear OOA(2593, 32552, F25, 24, 24) (dual of [(32552, 24), 781155, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2593, 390624, F25, 24) (dual of [390624, 390531, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2593, 390624, F25, 24) (dual of [390624, 390531, 25]-code), using
- net defined by OOA [i] based on linear OOA(2593, 32552, F25, 24, 24) (dual of [(32552, 24), 781155, 25]-NRT-code), using
- digital (0, 12, 26)-net over F25, using
(81, 81+24, 946565)-Net over F25 — Digital
Digital (81, 105, 946565)-net over F25, using
(81, 81+24, large)-Net in Base 25 — Upper bound on s
There is no (81, 105, large)-net in base 25, because
- 22 times m-reduction [i] would yield (81, 83, large)-net in base 25, but