Best Known (72−30, 72, s)-Nets in Base 3
(72−30, 72, 68)-Net over F3 — Constructive and digital
Digital (42, 72, 68)-net over F3, using
- trace code for nets [i] based on digital (6, 36, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
(72−30, 72, 73)-Net over F3 — Digital
Digital (42, 72, 73)-net over F3, using
(72−30, 72, 612)-Net in Base 3 — Upper bound on s
There is no (42, 72, 613)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 22999 381337 875004 160962 921104 656891 > 372 [i]