Best Known (32−5, 32, s)-Nets in Base 27
(32−5, 32, large)-Net over F27 — Constructive and digital
Digital (27, 32, large)-net over F27, using
- 273 times duplication [i] based on digital (24, 29, large)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 6, large)-net over F27, using
- digital (18, 23, 4194329)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- digital (16, 21, 4194301)-net over F27, using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- (u, u+v)-construction [i] based on
(32−5, 32, large)-Net in Base 27 — Upper bound on s
There is no (27, 32, large)-net in base 27, because
- 3 times m-reduction [i] would yield (27, 29, large)-net in base 27, but