Best Known (50, 50+38, s)-Nets in Base 3
(50, 50+38, 68)-Net over F3 — Constructive and digital
Digital (50, 88, 68)-net over F3, using
- trace code for nets [i] based on digital (6, 44, 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
(50, 50+38, 77)-Net over F3 — Digital
Digital (50, 88, 77)-net over F3, using
(50, 50+38, 624)-Net in Base 3 — Upper bound on s
There is no (50, 88, 625)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 986474 021512 942660 689588 114451 984080 052251 > 388 [i]