Best Known (54, 82, s)-Nets in Base 3
(54, 82, 128)-Net over F3 — Constructive and digital
Digital (54, 82, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 41, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
(54, 82, 144)-Net over F3 — Digital
Digital (54, 82, 144)-net over F3, using
(54, 82, 1870)-Net in Base 3 — Upper bound on s
There is no (54, 82, 1871)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1338 527511 867597 301797 884591 557709 479941 > 382 [i]