Best Known (54, 78, s)-Nets in Base 3
(54, 78, 144)-Net over F3 — Constructive and digital
Digital (54, 78, 144)-net over F3, using
- trace code for nets [i] based on digital (2, 26, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
(54, 78, 195)-Net over F3 — Digital
Digital (54, 78, 195)-net over F3, using
(54, 78, 3327)-Net in Base 3 — Upper bound on s
There is no (54, 78, 3328)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 16 450325 180491 529563 330473 065881 106433 > 378 [i]