MinT - Best Known (164, 164+69, s)-Nets in Base 3

Best Known (164, 164+69, s)-Nets in Base 3

(164, 164+69, 252)-Net over F₃ — Constructive and digital

Digital (164, 233, 252)-net over F₃, using

1 times m-reduction [i] based on digital (164, 234, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 78, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(164, 164+69, 528)-Net over F₃ — Digital

Digital (164, 233, 528)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+69, 12159)-Net in Base 3 — Upper bound on s

There is no (164, 233, 12160)-net in base 3, because

1 times m-reduction [i] would yield (164, 232, 12160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 493 371166 044908 352165 331864 164459 025946 165162 581349 251508 861770 191786 854336 805055 303222 432485 136206 451276 070145 > 3²³² [i]