Best Known (19, 19+8, s)-Nets in Base 27
(19, 19+8, 4959)-Net over F27 — Constructive and digital
Digital (19, 27, 4959)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (14, 22, 4921)-net over F27, using
- net defined by OOA [i] based on linear OOA(2722, 4921, F27, 8, 8) (dual of [(4921, 8), 39346, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2722, 19684, F27, 8) (dual of [19684, 19662, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(2722, 19683, F27, 8) (dual of [19683, 19661, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2719, 19683, F27, 7) (dual of [19683, 19664, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2722, 19684, F27, 8) (dual of [19684, 19662, 9]-code), using
- net defined by OOA [i] based on linear OOA(2722, 4921, F27, 8, 8) (dual of [(4921, 8), 39346, 9]-NRT-code), using
- digital (1, 5, 38)-net over F27, using
(19, 19+8, 43147)-Net over F27 — Digital
Digital (19, 27, 43147)-net over F27, using
(19, 19+8, large)-Net in Base 27 — Upper bound on s
There is no (19, 27, large)-net in base 27, because
- 6 times m-reduction [i] would yield (19, 21, large)-net in base 27, but