MinT - Best Known (165, 165+59, s)-Nets in Base 3

Best Known (165, 165+59, s)-Nets in Base 3

(165, 165+59, 288)-Net over F₃ — Constructive and digital

Digital (165, 224, 288)-net over F₃, using

7 times m-reduction [i] based on digital (165, 231, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 77, 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]

(165, 165+59, 765)-Net over F₃ — Digital

Digital (165, 224, 765)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+59, 27197)-Net in Base 3 — Upper bound on s

There is no (165, 224, 27198)-net in base 3, because

1 times m-reduction [i] would yield (165, 223, 27198)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25008 517558 981443 288246 807115 174326 665204 208698 005765 349429 924975 269879 430365 218811 890658 558762 271160 906853 > 3²²³ [i]