Best Known (20−6, 20, s)-Nets in Base 27
(20−6, 20, 7292)-Net over F27 — Constructive and digital
Digital (14, 20, 7292)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 730)-net over F27, using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(274, 730, F27, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- digital (10, 16, 6562)-net over F27, using
- net defined by OOA [i] based on linear OOA(2716, 6562, F27, 6, 6) (dual of [(6562, 6), 39356, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2716, 19686, F27, 6) (dual of [19686, 19670, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2716, 19683, F27, 6) (dual of [19683, 19667, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2713, 19683, F27, 5) (dual of [19683, 19670, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(2716, 19686, F27, 6) (dual of [19686, 19670, 7]-code), using
- net defined by OOA [i] based on linear OOA(2716, 6562, F27, 6, 6) (dual of [(6562, 6), 39356, 7]-NRT-code), using
- digital (1, 4, 730)-net over F27, using
(20−6, 20, 53252)-Net over F27 — Digital
Digital (14, 20, 53252)-net over F27, using
(20−6, 20, large)-Net in Base 27 — Upper bound on s
There is no (14, 20, large)-net in base 27, because
- 4 times m-reduction [i] would yield (14, 16, large)-net in base 27, but