Best Known (20, 20+23, s)-Nets in Base 27
(20, 20+23, 132)-Net over F27 — Constructive and digital
Digital (20, 43, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 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, 28, 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, 15, 64)-net over F27, using
(20, 20+23, 172)-Net in Base 27 — Constructive
(20, 43, 172)-net in base 27, using
- 9 times m-reduction [i] based on (20, 52, 172)-net in base 27, using
- base change [i] based on digital (7, 39, 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, 39, 172)-net over F81, using
(20, 20+23, 230)-Net over F27 — Digital
Digital (20, 43, 230)-net over F27, using
(20, 20+23, 244)-Net in Base 27
(20, 43, 244)-net in base 27, using
- 1 times m-reduction [i] based on (20, 44, 244)-net in base 27, using
- base change [i] based on digital (9, 33, 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, 33, 244)-net over F81, using
(20, 20+23, 55106)-Net in Base 27 — Upper bound on s
There is no (20, 43, 55107)-net in base 27, because
- 1 times m-reduction [i] would yield (20, 42, 55107)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 310073 496402 248646 450271 935898 396508 438445 610390 486515 812019 > 2742 [i]