Best Known (23, 23+36, s)-Nets in Base 27
(23, 23+36, 114)-Net over F27 — Constructive and digital
Digital (23, 59, 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+36, 163)-Net over F27 — Digital
Digital (23, 59, 163)-net over F27, using
- t-expansion [i] based on digital (21, 59, 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+36, 172)-Net in Base 27 — Constructive
(23, 59, 172)-net in base 27, using
- 5 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+36, 226)-Net in Base 27
(23, 59, 226)-net in base 27, using
- 1 times m-reduction [i] based on (23, 60, 226)-net in base 27, using
- base change [i] based on digital (8, 45, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- base change [i] based on digital (8, 45, 226)-net over F81, using
(23, 23+36, 14274)-Net in Base 27 — Upper bound on s
There is no (23, 59, 14275)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2 822155 150094 667410 169443 075985 754185 741749 548506 395486 575759 961076 724251 123152 459221 > 2759 [i]