Best Known (24, 24+10, s)-Nets in Base 27
(24, 24+10, 3975)-Net over F27 — Constructive and digital
Digital (24, 34, 3975)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (18, 28, 3937)-net over F27, using
- net defined by OOA [i] based on linear OOA(2728, 3937, F27, 10, 10) (dual of [(3937, 10), 39342, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2728, 19685, F27, 10) (dual of [19685, 19657, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2728, 19686, F27, 10) (dual of [19686, 19658, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(2728, 19683, F27, 10) (dual of [19683, 19655, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2725, 19683, F27, 9) (dual of [19683, 19658, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(2728, 19686, F27, 10) (dual of [19686, 19658, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2728, 19685, F27, 10) (dual of [19685, 19657, 11]-code), using
- net defined by OOA [i] based on linear OOA(2728, 3937, F27, 10, 10) (dual of [(3937, 10), 39342, 11]-NRT-code), using
- digital (1, 6, 38)-net over F27, using
(24, 24+10, 40757)-Net over F27 — Digital
Digital (24, 34, 40757)-net over F27, using
(24, 24+10, large)-Net in Base 27 — Upper bound on s
There is no (24, 34, large)-net in base 27, because
- 8 times m-reduction [i] would yield (24, 26, large)-net in base 27, but