MinT - Best Known (212−54, 212, s)-Nets in Base 3

Best Known (212−54, 212, s)-Nets in Base 3

(212−54, 212, 288)-Net over F₃ — Constructive and digital

Digital (158, 212, 288)-net over F₃, using

t-expansion [i] based on digital (157, 212, 288)-net over F₃, using
- 7 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 73, 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]

(212−54, 212, 828)-Net over F₃ — Digital

Digital (158, 212, 828)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−54, 212, 30428)-Net in Base 3 — Upper bound on s

There is no (158, 212, 30429)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141188 133548 796772 399076 724635 522256 518359 277105 564671 319686 024753 117713 778931 713773 305697 281181 812459 > 3²¹² [i]