Best Known (15, 15+7, s)-Nets in Base 27
(15, 15+7, 6589)-Net over F27 — Constructive and digital
Digital (15, 22, 6589)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (12, 19, 6561)-net over F27, using
- net defined by OOA [i] based on linear OOA(2719, 6561, F27, 7, 7) (dual of [(6561, 7), 45908, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2719, 19684, F27, 7) (dual of [19684, 19665, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding and stacking with additional row [i] based on linear OA(2719, 19684, F27, 7) (dual of [19684, 19665, 8]-code), using
- net defined by OOA [i] based on linear OOA(2719, 6561, F27, 7, 7) (dual of [(6561, 7), 45908, 8]-NRT-code), using
- digital (0, 3, 28)-net over F27, using
(15, 15+7, 20401)-Net over F27 — Digital
Digital (15, 22, 20401)-net over F27, using
(15, 15+7, large)-Net in Base 27 — Upper bound on s
There is no (15, 22, large)-net in base 27, because
- 5 times m-reduction [i] would yield (15, 17, large)-net in base 27, but