Best Known (73−43, 73, s)-Nets in Base 27
(73−43, 73, 132)-Net over F27 — Constructive and digital
Digital (30, 73, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 25, 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, 48, 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, 25, 64)-net over F27, using
(73−43, 73, 172)-Net in Base 27 — Constructive
(30, 73, 172)-net in base 27, using
- 19 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 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, 69, 172)-net over F81, using
(73−43, 73, 208)-Net over F27 — Digital
Digital (30, 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
(73−43, 73, 244)-Net in Base 27
(30, 73, 244)-net in base 27, using
- 11 times m-reduction [i] based on (30, 84, 244)-net in base 27, using
- base change [i] based on digital (9, 63, 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, 63, 244)-net over F81, using
(73−43, 73, 26969)-Net in Base 27 — Upper bound on s
There is no (30, 73, 26970)-net in base 27, because
- 1 times m-reduction [i] would yield (30, 72, 26970)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 11 435362 526479 679403 165956 682582 017572 622207 161735 279950 372820 358213 239026 483689 787699 510901 229402 144477 > 2772 [i]