Best Known (73−46, 73, s)-Nets in Base 27
(73−46, 73, 114)-Net over F27 — Constructive and digital
Digital (27, 73, 114)-net over F27, using
- t-expansion [i] based on digital (23, 73, 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
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(73−46, 73, 172)-Net in Base 27 — Constructive
(27, 73, 172)-net in base 27, using
- 7 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 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, 60, 172)-net over F81, using
(73−46, 73, 208)-Net over F27 — Digital
Digital (27, 73, 208)-net over F27, using
- t-expansion [i] based on digital (24, 73, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(73−46, 73, 226)-Net in Base 27
(27, 73, 226)-net in base 27, using
- 3 times m-reduction [i] based on (27, 76, 226)-net in base 27, using
- base change [i] based on digital (8, 57, 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, 57, 226)-net over F81, using
(73−46, 73, 12650)-Net in Base 27 — Upper bound on s
There is no (27, 73, 12651)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 309 130257 601158 872753 146795 761667 719502 036875 074260 085855 703744 057963 366688 528534 820773 035906 387203 576763 > 2773 [i]