MinT - Best Known (167, 167+57, s)-Nets in Base 3

Best Known (167, 167+57, s)-Nets in Base 3

(167, 167+57, 288)-Net over F₃ — Constructive and digital

Digital (167, 224, 288)-net over F₃, using

10 times m-reduction [i] based on digital (167, 234, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 78, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(167, 167+57, 871)-Net over F₃ — Digital

Digital (167, 224, 871)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+57, 35609)-Net in Base 3 — Upper bound on s

There is no (167, 224, 35610)-net in base 3, because

1 times m-reduction [i] would yield (167, 223, 35610)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25009 123988 596834 641569 653623 855860 688782 529823 331912 686084 839488 587397 825204 044016 589089 345090 868957 807641 > 3²²³ [i]