Best Known (34, 34+10, s)-Nets in Base 27
(34, 34+10, 106640)-Net over F27 — Constructive and digital
Digital (34, 44, 106640)-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 (27, 37, 106289)-net over F27, using
- net defined by OOA [i] based on linear OOA(2737, 106289, F27, 10, 10) (dual of [(106289, 10), 1062853, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2737, 531445, F27, 10) (dual of [531445, 531408, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(2737, 531441, F27, 10) (dual of [531441, 531404, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(9) ⊂ Ce(8) [i] based on
- OA 5-folding and stacking [i] based on linear OA(2737, 531445, F27, 10) (dual of [531445, 531408, 11]-code), using
- net defined by OOA [i] based on linear OOA(2737, 106289, F27, 10, 10) (dual of [(106289, 10), 1062853, 11]-NRT-code), using
- digital (2, 7, 351)-net over F27, using
(34, 34+10, 1586930)-Net over F27 — Digital
Digital (34, 44, 1586930)-net over F27, using
(34, 34+10, large)-Net in Base 27 — Upper bound on s
There is no (34, 44, large)-net in base 27, because
- 8 times m-reduction [i] would yield (34, 36, large)-net in base 27, but