Best Known (73−37, 73, s)-Nets in Base 27
(73−37, 73, 178)-Net over F27 — Constructive and digital
Digital (36, 73, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 26, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 47, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (8, 26, 84)-net over F27, using
(73−37, 73, 370)-Net in Base 27 — Constructive
(36, 73, 370)-net in base 27, using
- 7 times m-reduction [i] based on (36, 80, 370)-net in base 27, using
- base change [i] based on digital (16, 60, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 60, 370)-net over F81, using
(73−37, 73, 455)-Net over F27 — Digital
Digital (36, 73, 455)-net over F27, using
(73−37, 73, 154378)-Net in Base 27 — Upper bound on s
There is no (36, 73, 154379)-net in base 27, because
- 1 times m-reduction [i] would yield (36, 72, 154379)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 11 434909 091434 376790 687290 471463 256221 652300 971107 331755 184925 852027 624983 430453 579376 785292 799146 567269 > 2772 [i]