Best Known (30, 30+38, s)-Nets in Base 27
(30, 30+38, 146)-Net over F27 — Constructive and digital
Digital (30, 68, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 23, 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 (7, 45, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 23, 64)-net over F27, using
(30, 30+38, 224)-Net in Base 27 — Constructive
(30, 68, 224)-net in base 27, using
- base change [i] based on digital (13, 51, 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
(30, 30+38, 239)-Net over F27 — Digital
Digital (30, 68, 239)-net over F27, using
(30, 30+38, 298)-Net in Base 27
(30, 68, 298)-net in base 27, using
- 4 times m-reduction [i] based on (30, 72, 298)-net in base 27, using
- base change [i] based on digital (12, 54, 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, 54, 298)-net over F81, using
(30, 30+38, 40449)-Net in Base 27 — Upper bound on s
There is no (30, 68, 40450)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 21 519672 721077 733707 967075 899780 258685 005742 667539 810026 607947 585327 913956 605141 512728 869196 280161 > 2768 [i]