Best Known (55, 78, s)-Nets in Base 25
(55, 78, 1446)-Net over F25 — Constructive and digital
Digital (55, 78, 1446)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 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 (44, 67, 1420)-net over F25, using
- net defined by OOA [i] based on linear OOA(2567, 1420, F25, 23, 23) (dual of [(1420, 23), 32593, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2567, 15621, F25, 23) (dual of [15621, 15554, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2567, 15621, F25, 23) (dual of [15621, 15554, 24]-code), using
- net defined by OOA [i] based on linear OOA(2567, 1420, F25, 23, 23) (dual of [(1420, 23), 32593, 24]-NRT-code), using
- digital (0, 11, 26)-net over F25, using
(55, 78, 34128)-Net over F25 — Digital
Digital (55, 78, 34128)-net over F25, using
(55, 78, large)-Net in Base 25 — Upper bound on s
There is no (55, 78, large)-net in base 25, because
- 21 times m-reduction [i] would yield (55, 57, large)-net in base 25, but