Best Known (70−38, 70, s)-Nets in Base 27
(70−38, 70, 158)-Net over F27 — Constructive and digital
Digital (32, 70, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 25, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-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 (6, 25, 76)-net over F27, using
(70−38, 70, 224)-Net in Base 27 — Constructive
(32, 70, 224)-net in base 27, using
- 6 times m-reduction [i] based on (32, 76, 224)-net in base 27, using
- base change [i] based on digital (13, 57, 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, 57, 224)-net over F81, using
(70−38, 70, 290)-Net over F27 — Digital
Digital (32, 70, 290)-net over F27, using
(70−38, 70, 298)-Net in Base 27
(32, 70, 298)-net in base 27, using
- 10 times m-reduction [i] based on (32, 80, 298)-net in base 27, using
- base change [i] based on digital (12, 60, 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, 60, 298)-net over F81, using
(70−38, 70, 57228)-Net in Base 27 — Upper bound on s
There is no (32, 70, 57229)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 15685 878268 722226 088971 421725 006175 264652 541519 234398 189175 127939 939563 294402 004546 981295 749115 463731 > 2770 [i]