Best Known (21, 21+28, s)-Nets in Base 27
(21, 21+28, 116)-Net over F27 — Constructive and digital
Digital (21, 49, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 32, 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 (3, 17, 52)-net over F27, using
(21, 21+28, 168)-Net over F27 — Digital
Digital (21, 49, 168)-net over F27, using
(21, 21+28, 172)-Net in Base 27 — Constructive
(21, 49, 172)-net in base 27, using
- 7 times m-reduction [i] based on (21, 56, 172)-net in base 27, using
- base change [i] based on digital (7, 42, 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, 42, 172)-net over F81, using
(21, 21+28, 226)-Net in Base 27
(21, 49, 226)-net in base 27, using
- 3 times m-reduction [i] based on (21, 52, 226)-net in base 27, using
- base change [i] based on digital (8, 39, 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
- base change [i] based on digital (8, 39, 226)-net over F81, using
(21, 21+28, 23775)-Net in Base 27 — Upper bound on s
There is no (21, 49, 23776)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 13707 590693 536390 512602 968140 106636 671767 177219 451581 238576 882503 828289 > 2749 [i]