Best Known (31, 77, s)-Nets in Base 27
(31, 77, 128)-Net over F27 — Constructive and digital
Digital (31, 77, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 27, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 50, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 27, 64)-net over F27, using
(31, 77, 172)-Net in Base 27 — Constructive
(31, 77, 172)-net in base 27, using
- 19 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 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, 72, 172)-net over F81, using
(31, 77, 208)-Net over F27 — Digital
Digital (31, 77, 208)-net over F27, using
- t-expansion [i] based on digital (24, 77, 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
(31, 77, 244)-Net in Base 27
(31, 77, 244)-net in base 27, using
- 11 times m-reduction [i] based on (31, 88, 244)-net in base 27, using
- base change [i] based on digital (9, 66, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 66, 244)-net over F81, using
(31, 77, 22449)-Net in Base 27 — Upper bound on s
There is no (31, 77, 22450)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 164 117296 780049 754274 376283 480871 743051 745730 998003 944353 156541 537653 712044 498022 625107 563338 122006 656851 672761 > 2777 [i]