Best Known (165, 243, s)-Nets in Base 3
(165, 243, 172)-Net over F3 — Constructive and digital
Digital (165, 243, 172)-net over F3, using
- 1 times m-reduction [i] based on digital (165, 244, 172)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 52, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- digital (113, 192, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 96, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- trace code for nets [i] based on digital (17, 96, 74)-net over F9, using
- digital (13, 52, 24)-net over F3, using
- (u, u+v)-construction [i] based on
(165, 243, 424)-Net over F3 — Digital
Digital (165, 243, 424)-net over F3, using
(165, 243, 7193)-Net in Base 3 — Upper bound on s
There is no (165, 243, 7194)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 87 626235 532120 289897 705871 247086 828339 073291 520966 325263 250675 714376 833584 284207 754002 709958 237547 783577 998380 931017 > 3243 [i]