Best Known (80−52, 80, s)-Nets in Base 27
(80−52, 80, 114)-Net over F27 — Constructive and digital
Digital (28, 80, 114)-net over F27, using
- t-expansion [i] based on digital (23, 80, 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
(80−52, 80, 172)-Net in Base 27 — Constructive
(28, 80, 172)-net in base 27, using
- 4 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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, 63, 172)-net over F81, using
(80−52, 80, 208)-Net over F27 — Digital
Digital (28, 80, 208)-net over F27, using
- t-expansion [i] based on digital (24, 80, 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
(80−52, 80, 226)-Net in Base 27
(28, 80, 226)-net in base 27, using
- base change [i] based on digital (8, 60, 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
(80−52, 80, 10278)-Net in Base 27 — Upper bound on s
There is no (28, 80, 10279)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 230177 647531 380386 459603 376400 828026 452790 918467 890487 510939 065015 712055 671592 945841 107101 554395 143227 185135 505965 > 2780 [i]