Best Known (70, 70+30, s)-Nets in Base 27
(70, 70+30, 1340)-Net over F27 — Constructive and digital
Digital (70, 100, 1340)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 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 (55, 85, 1312)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- digital (0, 15, 28)-net over F27, using
(70, 70+30, 38730)-Net over F27 — Digital
Digital (70, 100, 38730)-net over F27, using
(70, 70+30, large)-Net in Base 27 — Upper bound on s
There is no (70, 100, large)-net in base 27, because
- 28 times m-reduction [i] would yield (70, 72, large)-net in base 27, but