Best Known (47, 59, s)-Nets in Base 27
(47, 59, 1398100)-Net over F27 — Constructive and digital
Digital (47, 59, 1398100)-net over F27, using
- 273 times duplication [i] based on digital (44, 56, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2756, 1398100, F27, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2756, 8388600, F27, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2756, 8388600, F27, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(2756, 1398100, F27, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
(47, 59, large)-Net over F27 — Digital
Digital (47, 59, large)-net over F27, using
- 273 times duplication [i] based on digital (44, 56, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
(47, 59, large)-Net in Base 27 — Upper bound on s
There is no (47, 59, large)-net in base 27, because
- 10 times m-reduction [i] would yield (47, 49, large)-net in base 27, but