MinT - Best Known (176−47, 176, s)-Nets in Base 3

Best Known (176−47, 176, s)-Nets in Base 3

(176−47, 176, 288)-Net over F₃ — Constructive and digital

Digital (129, 176, 288)-net over F₃, using

1 times m-reduction [i] based on digital (129, 177, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 59, 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]

(176−47, 176, 595)-Net over F₃ — Digital

Digital (129, 176, 595)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−47, 176, 20100)-Net in Base 3 — Upper bound on s

There is no (129, 176, 20101)-net in base 3, because

1 times m-reduction [i] would yield (129, 175, 20101)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313596 471378 529752 148952 858187 178466 236045 601734 629210 864599 711722 790706 343996 477467 > 3¹⁷⁵ [i]