Best Known (21, 21+6, s)-Nets in Base 27
(21, 21+6, 2796201)-Net over F27 — Constructive and digital
Digital (21, 27, 2796201)-net over F27, using
- 271 times duplication [i] based on 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
(21, 21+6, large)-Net over F27 — Digital
Digital (21, 27, large)-net over F27, using
- 271 times duplication [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
(21, 21+6, large)-Net in Base 27 — Upper bound on s
There is no (21, 27, large)-net in base 27, because
- 4 times m-reduction [i] would yield (21, 23, large)-net in base 27, but