Best Known (58, 82, s)-Nets in Base 25
(58, 82, 1328)-Net over F25 — Constructive and digital
Digital (58, 82, 1328)-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 (46, 70, 1302)-net over F25, using
- net defined by OOA [i] based on linear OOA(2570, 1302, F25, 24, 24) (dual of [(1302, 24), 31178, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2570, 15624, F25, 24) (dual of [15624, 15554, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2570, 15624, F25, 24) (dual of [15624, 15554, 25]-code), using
- net defined by OOA [i] based on linear OOA(2570, 1302, F25, 24, 24) (dual of [(1302, 24), 31178, 25]-NRT-code), using
- digital (0, 12, 26)-net over F25, using
(58, 82, 37874)-Net over F25 — Digital
Digital (58, 82, 37874)-net over F25, using
(58, 82, large)-Net in Base 25 — Upper bound on s
There is no (58, 82, large)-net in base 25, because
- 22 times m-reduction [i] would yield (58, 60, large)-net in base 25, but