Best Known (167, 167+56, s)-Nets in Base 3
(167, 167+56, 324)-Net over F3 — Constructive and digital
Digital (167, 223, 324)-net over F3, using
- 31 times duplication [i] based on 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
- trace code for nets [i] based on digital (18, 74, 108)-net over F27, using
(167, 167+56, 913)-Net over F3 — Digital
Digital (167, 223, 913)-net over F3, using
(167, 167+56, 35609)-Net in Base 3 — Upper bound on s
There is no (167, 223, 35610)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25009 123988 596834 641569 653623 855860 688782 529823 331912 686084 839488 587397 825204 044016 589089 345090 868957 807641 > 3223 [i]