Best Known (60, 60+54, s)-Nets in Base 3
(60, 60+54, 56)-Net over F3 — Constructive and digital
Digital (60, 114, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 57, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
(60, 60+54, 73)-Net over F3 — Digital
Digital (60, 114, 73)-net over F3, using
(60, 60+54, 538)-Net in Base 3 — Upper bound on s
There is no (60, 114, 539)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 488862 882833 081300 539924 212058 638571 065105 831800 985435 > 3114 [i]