Best Known (35, 45, s)-Nets in Base 27
(35, 45, 106641)-Net over F27 — Constructive and digital
Digital (35, 45, 106641)-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 (28, 38, 106290)-net over F27, using
- net defined by OOA [i] based on linear OOA(2738, 106290, F27, 10, 10) (dual of [(106290, 10), 1062862, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2738, 531450, F27, 10) (dual of [531450, 531412, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [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(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(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- OA 5-folding and stacking [i] based on linear OA(2738, 531450, F27, 10) (dual of [531450, 531412, 11]-code), using
- net defined by OOA [i] based on linear OOA(2738, 106290, F27, 10, 10) (dual of [(106290, 10), 1062862, 11]-NRT-code), using
- digital (2, 7, 351)-net over F27, using
(35, 45, 2288747)-Net over F27 — Digital
Digital (35, 45, 2288747)-net over F27, using
(35, 45, large)-Net in Base 27 — Upper bound on s
There is no (35, 45, large)-net in base 27, because
- 8 times m-reduction [i] would yield (35, 37, large)-net in base 27, but