Best Known (166, 222, s)-Nets in Base 3
(166, 222, 324)-Net over F3 — Constructive and digital
Digital (166, 222, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 74, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(166, 222, 894)-Net over F3 — Digital
Digital (166, 222, 894)-net over F3, using
(166, 222, 34238)-Net in Base 3 — Upper bound on s
There is no (166, 222, 34239)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8337 747078 858226 728876 133164 744506 676534 715377 602282 576422 355304 919026 757535 937547 762053 123837 566067 246025 > 3222 [i]