MinT - Best Known (226−58, 226, s)-Nets in Base 3

Best Known (226−58, 226, s)-Nets in Base 3

(226−58, 226, 288)-Net over F₃ — Constructive and digital

Digital (168, 226, 288)-net over F₃, using

t-expansion [i] based on digital (167, 226, 288)-net over F₃, using
- 8 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]

(226−58, 226, 849)-Net over F₃ — Digital

Digital (168, 226, 849)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−58, 226, 30474)-Net in Base 3 — Upper bound on s

There is no (168, 226, 30475)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675253 733818 864490 215477 421649 675294 038330 371571 211182 267078 571738 499444 663807 617850 706877 018867 845757 211359 > 3²²⁶ [i]