Best Known (82−19, 82, s)-Nets in Base 27
(82−19, 82, 59077)-Net over F27 — Constructive and digital
Digital (63, 82, 59077)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (54, 73, 59049)-net over F27, using
- net defined by OOA [i] based on linear OOA(2773, 59049, F27, 19, 19) (dual of [(59049, 19), 1121858, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2773, 531442, F27, 19) (dual of [531442, 531369, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, 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(2773, 531442, F27, 19) (dual of [531442, 531369, 20]-code), using
- net defined by OOA [i] based on linear OOA(2773, 59049, F27, 19, 19) (dual of [(59049, 19), 1121858, 20]-NRT-code), using
- digital (0, 9, 28)-net over F27, using
(82−19, 82, 963425)-Net over F27 — Digital
Digital (63, 82, 963425)-net over F27, using
(82−19, 82, large)-Net in Base 27 — Upper bound on s
There is no (63, 82, large)-net in base 27, because
- 17 times m-reduction [i] would yield (63, 65, large)-net in base 27, but