Best Known (40, 40+56, s)-Nets in Base 27
(40, 40+56, 152)-Net over F27 — Constructive and digital
Digital (40, 96, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 34, 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 (6, 62, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 34, 76)-net over F27, using
(40, 40+56, 273)-Net over F27 — Digital
Digital (40, 96, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
(40, 40+56, 370)-Net in Base 27 — Constructive
(40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 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
(40, 40+56, 35106)-Net in Base 27 — Upper bound on s
There is no (40, 96, 35107)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 257741 675806 404035 734391 103020 921918 095374 182685 707125 705192 304558 383256 204632 169660 561458 451666 391494 358350 454025 512899 306651 852826 377865 > 2796 [i]