Best Known (32−6, 32, s)-Nets in Base 27
(32−6, 32, 2816697)-Net over F27 — Constructive and digital
Digital (26, 32, 2816697)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 6, 20496)-net over F27, using
- net defined by OOA [i] based on linear OOA(276, 20496, F27, 3, 3) (dual of [(20496, 3), 61482, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(276, 20496, F27, 2, 3) (dual of [(20496, 2), 40986, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(276, 20496, F27, 3, 3) (dual of [(20496, 3), 61482, 4]-NRT-code), using
- digital (20, 26, 2796201)-net over F27, using
- net defined by OOA [i] based on linear OOA(2726, 2796201, F27, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2726, 2796201, F27, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- digital (3, 6, 20496)-net over F27, using
(32−6, 32, large)-Net over F27 — Digital
Digital (26, 32, large)-net over F27, using
- 271 times duplication [i] based on digital (25, 31, large)-net over F27, using
- t-expansion [i] based on digital (24, 31, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- t-expansion [i] based on digital (24, 31, large)-net over F27, using
(32−6, 32, large)-Net in Base 27 — Upper bound on s
There is no (26, 32, large)-net in base 27, because
- 4 times m-reduction [i] would yield (26, 28, large)-net in base 27, but