Best Known (73−39, 73, s)-Nets in Base 27
(73−39, 73, 166)-Net over F27 — Constructive and digital
Digital (34, 73, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 26, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (8, 47, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 26, 82)-net over F27, using
(73−39, 73, 224)-Net in Base 27 — Constructive
(34, 73, 224)-net in base 27, using
- 11 times m-reduction [i] based on (34, 84, 224)-net in base 27, using
- base change [i] based on digital (13, 63, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 63, 224)-net over F81, using
(73−39, 73, 328)-Net over F27 — Digital
Digital (34, 73, 328)-net over F27, using
(73−39, 73, 80966)-Net in Base 27 — Upper bound on s
There is no (34, 73, 80967)-net in base 27, because
- 1 times m-reduction [i] would yield (34, 72, 80967)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 11 435193 250255 026870 941236 847489 180552 705548 081820 036079 374233 974025 920426 727997 213890 716399 702790 404979 > 2772 [i]