Best Known (42, 42+28, s)-Nets in Base 3
(42, 42+28, 72)-Net over F3 — Constructive and digital
Digital (42, 70, 72)-net over F3, using
- trace code for nets [i] based on digital (7, 35, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
(42, 42+28, 81)-Net over F3 — Digital
Digital (42, 70, 81)-net over F3, using
(42, 42+28, 721)-Net in Base 3 — Upper bound on s
There is no (42, 70, 722)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2542 837933 038352 389080 767412 669037 > 370 [i]