Best Known (57−17, 57, s)-Nets in Base 27
(57−17, 57, 2488)-Net over F27 — Constructive and digital
Digital (40, 57, 2488)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (32, 49, 2460)-net over F27, using
- net defined by OOA [i] based on linear OOA(2749, 2460, F27, 17, 17) (dual of [(2460, 17), 41771, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2749, 19681, F27, 17) (dual of [19681, 19632, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2749, 19681, F27, 17) (dual of [19681, 19632, 18]-code), using
- net defined by OOA [i] based on linear OOA(2749, 2460, F27, 17, 17) (dual of [(2460, 17), 41771, 18]-NRT-code), using
- digital (0, 8, 28)-net over F27, using
(57−17, 57, 32878)-Net over F27 — Digital
Digital (40, 57, 32878)-net over F27, using
(57−17, 57, large)-Net in Base 27 — Upper bound on s
There is no (40, 57, large)-net in base 27, because
- 15 times m-reduction [i] would yield (40, 42, large)-net in base 27, but