Best Known (27−5, 27, s)-Nets in Base 27
(27−5, 27, 8388602)-Net over F27 — Constructive and digital
Digital (22, 27, 8388602)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 6, large)-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
(27−5, 27, large)-Net over F27 — Digital
Digital (22, 27, large)-net over F27, using
- 271 times duplication [i] based on digital (21, 26, large)-net over F27, using
- t-expansion [i] based on digital (20, 26, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [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]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- t-expansion [i] based on digital (20, 26, large)-net over F27, using
(27−5, 27, large)-Net in Base 27 — Upper bound on s
There is no (22, 27, large)-net in base 27, because
- 3 times m-reduction [i] would yield (22, 24, large)-net in base 27, but