Best Known (29, 29+40, s)-Nets in Base 27
(29, 29+40, 132)-Net over F27 — Constructive and digital
Digital (29, 69, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 24, 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 (5, 45, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 24, 64)-net over F27, using
(29, 29+40, 172)-Net in Base 27 — Constructive
(29, 69, 172)-net in base 27, using
- 19 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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, 66, 172)-net over F81, using
(29, 29+40, 208)-Net over F27 — Digital
Digital (29, 69, 208)-net over F27, using
- t-expansion [i] based on digital (24, 69, 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
(29, 29+40, 244)-Net in Base 27
(29, 69, 244)-net in base 27, using
- 11 times m-reduction [i] based on (29, 80, 244)-net in base 27, using
- base change [i] based on digital (9, 60, 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, 60, 244)-net over F81, using
(29, 29+40, 27693)-Net in Base 27 — Upper bound on s
There is no (29, 69, 27694)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 581 133684 634336 337685 895745 713830 545752 941649 324358 695299 046396 699400 899711 615360 068108 555948 804777 > 2769 [i]