Best Known (33, 33+14, s)-Nets in Base 27
(33, 33+14, 2840)-Net over F27 — Constructive and digital
Digital (33, 47, 2840)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (26, 40, 2812)-net over F27, using
- net defined by OOA [i] based on linear OOA(2740, 2812, F27, 14, 14) (dual of [(2812, 14), 39328, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2740, 19684, F27, 14) (dual of [19684, 19644, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2740, 19686, F27, 14) (dual of [19686, 19646, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(2740, 19683, F27, 14) (dual of [19683, 19643, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2740, 19686, F27, 14) (dual of [19686, 19646, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2740, 19684, F27, 14) (dual of [19684, 19644, 15]-code), using
- net defined by OOA [i] based on linear OOA(2740, 2812, F27, 14, 14) (dual of [(2812, 14), 39328, 15]-NRT-code), using
- digital (0, 7, 28)-net over F27, using
(33, 33+14, 32617)-Net over F27 — Digital
Digital (33, 47, 32617)-net over F27, using
(33, 33+14, large)-Net in Base 27 — Upper bound on s
There is no (33, 47, large)-net in base 27, because
- 12 times m-reduction [i] would yield (33, 35, large)-net in base 27, but