Best Known (39−9, 39, s)-Nets in Base 27
(39−9, 39, 133212)-Net over F27 — Constructive and digital
Digital (30, 39, 133212)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(276, 351, F27, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(276, 702, F27, 4) (dual of [702, 696, 5]-code), using
- 1 times truncation [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(276, 702, F27, 4) (dual of [702, 696, 5]-code), using
- net defined by OOA [i] based on linear OOA(276, 351, F27, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
- digital (24, 33, 132861)-net over F27, using
- net defined by OOA [i] based on linear OOA(2733, 132861, F27, 9, 9) (dual of [(132861, 9), 1195716, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2733, 531445, F27, 9) (dual of [531445, 531412, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(2733, 531441, F27, 9) (dual of [531441, 531408, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 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(8) ⊂ Ce(7) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2733, 531445, F27, 9) (dual of [531445, 531412, 10]-code), using
- net defined by OOA [i] based on linear OOA(2733, 132861, F27, 9, 9) (dual of [(132861, 9), 1195716, 10]-NRT-code), using
- digital (2, 6, 351)-net over F27, using
(39−9, 39, 1375993)-Net over F27 — Digital
Digital (30, 39, 1375993)-net over F27, using
(39−9, 39, large)-Net in Base 27 — Upper bound on s
There is no (30, 39, large)-net in base 27, because
- 7 times m-reduction [i] would yield (30, 32, large)-net in base 27, but