Best Known (22, 22+40, s)-Nets in Base 27
(22, 22+40, 112)-Net over F27 — Constructive and digital
Digital (22, 62, 112)-net over F27, using
- net from sequence [i] based on digital (22, 111)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 22 and N(F) ≥ 112, using
(22, 22+40, 160)-Net in Base 27 — Constructive
(22, 62, 160)-net in base 27, using
- 6 times m-reduction [i] based on (22, 68, 160)-net in base 27, using
- base change [i] based on digital (5, 51, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 51, 160)-net over F81, using
(22, 22+40, 163)-Net over F27 — Digital
Digital (22, 62, 163)-net over F27, using
- t-expansion [i] based on digital (21, 62, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
(22, 22+40, 190)-Net in Base 27
(22, 62, 190)-net in base 27, using
- 2 times m-reduction [i] based on (22, 64, 190)-net in base 27, using
- base change [i] based on digital (6, 48, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 48, 190)-net over F81, using
(22, 22+40, 8730)-Net in Base 27 — Upper bound on s
There is no (22, 62, 8731)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 55568 608869 986612 731168 683590 417819 313696 468662 380895 253958 028884 203428 239691 690382 657753 > 2762 [i]