Best Known (68−30, 68, s)-Nets in Base 3
(68−30, 68, 60)-Net over F3 — Constructive and digital
Digital (38, 68, 60)-net over F3, using
- trace code for nets [i] based on digital (4, 34, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
(68−30, 68, 453)-Net in Base 3 — Upper bound on s
There is no (38, 68, 454)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 286 431344 391932 919334 089576 547017 > 368 [i]