Best Known (52−19, 52, s)-Nets in Base 27
(52−19, 52, 308)-Net over F27 — Constructive and digital
Digital (33, 52, 308)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 28)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 with arbitrarily large s, using
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27, using
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27 (see above)
- 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 (0, 3, 28)-net over F27 (see above)
- digital (0, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 9, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 19, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 1, 28)-net over F27, using
(52−19, 52, 729)-Net in Base 27 — Constructive
(33, 52, 729)-net in base 27, using
- base change [i] based on digital (20, 39, 729)-net over F81, using
- 812 times duplication [i] based on digital (18, 37, 729)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 729, F81, 19, 19) (dual of [(729, 19), 13814, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, 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(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using
- net defined by OOA [i] based on linear OOA(8137, 729, F81, 19, 19) (dual of [(729, 19), 13814, 20]-NRT-code), using
- 812 times duplication [i] based on digital (18, 37, 729)-net over F81, using
(52−19, 52, 3974)-Net over F27 — Digital
Digital (33, 52, 3974)-net over F27, using
(52−19, 52, large)-Net in Base 27 — Upper bound on s
There is no (33, 52, large)-net in base 27, because
- 17 times m-reduction [i] would yield (33, 35, large)-net in base 27, but