Best Known (25, 35, s)-Nets in Base 27
(25, 35, 4288)-Net over F27 — Constructive and digital
Digital (25, 35, 4288)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), 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 (2, 7, 351)-net over F27, using
(25, 35, 58779)-Net over F27 — Digital
Digital (25, 35, 58779)-net over F27, using
(25, 35, large)-Net in Base 27 — Upper bound on s
There is no (25, 35, large)-net in base 27, because
- 8 times m-reduction [i] would yield (25, 27, large)-net in base 27, but