MinT - Best Known (166, 166+67, s)-Nets in Base 3

Best Known (166, 166+67, s)-Nets in Base 3

(166, 166+67, 282)-Net over F₃ — Constructive and digital

Digital (166, 233, 282)-net over F₃, using

1 times m-reduction [i] based on digital (166, 234, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 78, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(166, 166+67, 581)-Net over F₃ — Digital

Digital (166, 233, 581)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+67, 14848)-Net in Base 3 — Upper bound on s

There is no (166, 233, 14849)-net in base 3, because

1 times m-reduction [i] would yield (166, 232, 14849)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 739106 032691 059781 950598 456759 484238 730799 703707 836686 159603 743815 607073 800645 043899 316991 310514 095714 774915 > 3²³² [i]