Best Known (30, 30+13, s)-Nets in Base 27
(30, 30+13, 3308)-Net over F27 — Constructive and digital
Digital (30, 43, 3308)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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 (24, 37, 3280)-net over F27, using
- net defined by OOA [i] based on linear OOA(2737, 3280, F27, 13, 13) (dual of [(3280, 13), 42603, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2737, 19681, F27, 13) (dual of [19681, 19644, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2737, 19683, F27, 13) (dual of [19683, 19646, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2737, 19683, F27, 13) (dual of [19683, 19646, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2737, 19681, F27, 13) (dual of [19681, 19644, 14]-code), using
- net defined by OOA [i] based on linear OOA(2737, 3280, F27, 13, 13) (dual of [(3280, 13), 42603, 14]-NRT-code), using
- digital (0, 6, 28)-net over F27, using
(30, 30+13, 27386)-Net over F27 — Digital
Digital (30, 43, 27386)-net over F27, using
(30, 30+13, large)-Net in Base 27 — Upper bound on s
There is no (30, 43, large)-net in base 27, because
- 11 times m-reduction [i] would yield (30, 32, large)-net in base 27, but