Best Known (186−42, 186, s)-Nets in Base 3
(186−42, 186, 600)-Net over F3 — Constructive and digital
Digital (144, 186, 600)-net over F3, using
- 32 times duplication [i] based on digital (142, 184, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 46, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 46, 150)-net over F81, using
(186−42, 186, 1199)-Net over F3 — Digital
Digital (144, 186, 1199)-net over F3, using
(186−42, 186, 72991)-Net in Base 3 — Upper bound on s
There is no (144, 186, 72992)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 55542 740060 133740 226957 125884 489092 946941 998715 664283 620440 535809 808384 801409 856366 906945 > 3186 [i]