Best Known (109, 109+42, s)-Nets in Base 3
(109, 109+42, 252)-Net over F3 — Constructive and digital
Digital (109, 151, 252)-net over F3, using
- 31 times duplication [i] based on digital (108, 150, 252)-net over F3, using
- trace code for nets [i] based on digital (8, 50, 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
- trace code for nets [i] based on digital (8, 50, 84)-net over F27, using
(109, 109+42, 453)-Net over F3 — Digital
Digital (109, 151, 453)-net over F3, using
(109, 109+42, 11679)-Net in Base 3 — Upper bound on s
There is no (109, 151, 11680)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 110624 206082 062026 116242 471396 891198 323995 754454 932696 273629 630896 463681 > 3151 [i]