Best Known (17−4, 17, s)-Nets in Base 27
(17−4, 17, 4194301)-Net over F27 — Constructive and digital
Digital (13, 17, 4194301)-net over F27, using
- 271 times duplication [i] based on digital (12, 16, 4194301)-net over F27, using
- net defined by OOA [i] based on linear OOA(2716, 4194301, F27, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2716, 8388602, F27, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2716, large, F27, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2716, large, F27, 4) (dual of [large, large−16, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(2716, 8388602, F27, 4) (dual of [8388602, 8388586, 5]-code), using
- net defined by OOA [i] based on linear OOA(2716, 4194301, F27, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
(17−4, 17, large)-Net over F27 — Digital
Digital (13, 17, large)-net over F27, using
- 271 times duplication [i] based on digital (12, 16, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2716, large, F27, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2716, large, F27, 4) (dual of [large, large−16, 5]-code), using
(17−4, 17, large)-Net in Base 27 — Upper bound on s
There is no (13, 17, large)-net in base 27, because
- 2 times m-reduction [i] would yield (13, 15, large)-net in base 27, but