Best Known (41−12, 41, s)-Nets in Base 27
(41−12, 41, 3319)-Net over F27 — Constructive and digital
Digital (29, 41, 3319)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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 (22, 34, 3281)-net over F27, using
- net defined by OOA [i] based on linear OOA(2734, 3281, F27, 12, 12) (dual of [(3281, 12), 39338, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2734, 19686, F27, 12) (dual of [19686, 19652, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(2734, 19683, F27, 12) (dual of [19683, 19649, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2731, 19683, F27, 11) (dual of [19683, 19652, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(2734, 19686, F27, 12) (dual of [19686, 19652, 13]-code), using
- net defined by OOA [i] based on linear OOA(2734, 3281, F27, 12, 12) (dual of [(3281, 12), 39338, 13]-NRT-code), using
- digital (1, 7, 38)-net over F27, using
(41−12, 41, 40849)-Net over F27 — Digital
Digital (29, 41, 40849)-net over F27, using
(41−12, 41, large)-Net in Base 27 — Upper bound on s
There is no (29, 41, large)-net in base 27, because
- 10 times m-reduction [i] would yield (29, 31, large)-net in base 27, but