Best Known (54, 54+40, s)-Nets in Base 3
(54, 54+40, 72)-Net over F3 — Constructive and digital
Digital (54, 94, 72)-net over F3, using
- trace code for nets [i] based on digital (7, 47, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
(54, 54+40, 85)-Net over F3 — Digital
Digital (54, 94, 85)-net over F3, using
(54, 54+40, 706)-Net in Base 3 — Upper bound on s
There is no (54, 94, 707)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 718 795986 233356 004421 350257 183788 032600 937657 > 394 [i]