Best Known (99−54, 99, s)-Nets in Base 27
(99−54, 99, 178)-Net over F27 — Constructive and digital
Digital (45, 99, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 35, 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, 64, 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, 35, 84)-net over F27, using
(99−54, 99, 367)-Net over F27 — Digital
Digital (45, 99, 367)-net over F27, using
(99−54, 99, 370)-Net in Base 27 — Constructive
(45, 99, 370)-net in base 27, using
- t-expansion [i] based on (43, 99, 370)-net in base 27, using
- 9 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- 9 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(99−54, 99, 74419)-Net in Base 27 — Upper bound on s
There is no (45, 99, 74420)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 5071 427702 538934 826953 484705 420889 122330 453500 246691 583884 450493 124776 680227 277592 853948 508004 809729 210539 889401 017029 587291 463092 179868 169233 > 2799 [i]