Best Known (23, 23+40, s)-Nets in Base 27
(23, 23+40, 114)-Net over F27 — Constructive and digital
Digital (23, 63, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
(23, 23+40, 163)-Net over F27 — Digital
Digital (23, 63, 163)-net over F27, using
- t-expansion [i] based on digital (21, 63, 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
(23, 23+40, 172)-Net in Base 27 — Constructive
(23, 63, 172)-net in base 27, using
- 1 times m-reduction [i] based on (23, 64, 172)-net in base 27, using
- base change [i] based on digital (7, 48, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 48, 172)-net over F81, using
(23, 23+40, 190)-Net in Base 27
(23, 63, 190)-net in base 27, using
- 5 times m-reduction [i] based on (23, 68, 190)-net in base 27, using
- base change [i] based on digital (6, 51, 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, 51, 190)-net over F81, using
(23, 23+40, 10296)-Net in Base 27 — Upper bound on s
There is no (23, 63, 10297)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 500419 731318 368510 702584 440271 043240 765539 180068 988882 551304 484498 460963 111876 068848 798961 > 2763 [i]