MinT - Best Known (225−58, 225, s)-Nets in Base 3

Best Known (225−58, 225, s)-Nets in Base 3

(225−58, 225, 288)-Net over F₃ — Constructive and digital

Digital (167, 225, 288)-net over F₃, using

9 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]

(225−58, 225, 832)-Net over F₃ — Digital

Digital (167, 225, 832)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−58, 225, 29340)-Net in Base 3 — Upper bound on s

There is no (167, 225, 29341)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225074 417757 239089 268727 579149 839759 356634 959154 216581 177752 475108 135303 172234 873306 426302 907711 667514 019179 > 3²²⁵ [i]