Best Known (47, 66, s)-Nets in Base 27
(47, 66, 2235)-Net over F27 — Constructive and digital
Digital (47, 66, 2235)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (36, 55, 2187)-net over F27, using
- net defined by OOA [i] based on linear OOA(2755, 2187, F27, 19, 19) (dual of [(2187, 19), 41498, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2755, 19684, F27, 19) (dual of [19684, 19629, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(2755, 19684, F27, 19) (dual of [19684, 19629, 20]-code), using
- net defined by OOA [i] based on linear OOA(2755, 2187, F27, 19, 19) (dual of [(2187, 19), 41498, 20]-NRT-code), using
- digital (2, 11, 48)-net over F27, using
(47, 66, 51471)-Net over F27 — Digital
Digital (47, 66, 51471)-net over F27, using
(47, 66, large)-Net in Base 27 — Upper bound on s
There is no (47, 66, large)-net in base 27, because
- 17 times m-reduction [i] would yield (47, 49, large)-net in base 27, but