Best Known (189−58, 189, s)-Nets in Base 3
(189−58, 189, 204)-Net over F3 — Constructive and digital
Digital (131, 189, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 63, 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
(189−58, 189, 393)-Net over F3 — Digital
Digital (131, 189, 393)-net over F3, using
(189−58, 189, 7480)-Net in Base 3 — Upper bound on s
There is no (131, 189, 7481)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 499598 578843 154425 070384 823902 791467 827589 339704 622789 665657 690079 222064 693912 459799 917571 > 3189 [i]