Best Known (37, 37+56, s)-Nets in Base 27
(37, 37+56, 132)-Net over F27 — Constructive and digital
Digital (37, 93, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- 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 (5, 61, 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, 32, 64)-net over F27, using
(37, 37+56, 224)-Net in Base 27 — Constructive
(37, 93, 224)-net in base 27, using
- 3 times m-reduction [i] based on (37, 96, 224)-net in base 27, using
- base change [i] based on digital (13, 72, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 72, 224)-net over F81, using
(37, 37+56, 244)-Net over F27 — Digital
Digital (37, 93, 244)-net over F27, using
- t-expansion [i] based on digital (36, 93, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(37, 37+56, 298)-Net in Base 27
(37, 93, 298)-net in base 27, using
- 7 times m-reduction [i] based on (37, 100, 298)-net in base 27, using
- base change [i] based on digital (12, 75, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 75, 298)-net over F81, using
(37, 37+56, 24657)-Net in Base 27 — Upper bound on s
There is no (37, 93, 24658)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 13 095385 705970 443613 284059 894686 096793 377279 454652 138425 175965 228153 640911 777851 483924 086813 133789 856553 571885 622354 685519 472379 574809 > 2793 [i]