MinT - Best Known (225−50, 225, s)-Nets in Base 3

Best Known (225−50, 225, s)-Nets in Base 3

(225−50, 225, 640)-Net over F₃ — Constructive and digital

Digital (175, 225, 640)-net over F₃, using

3¹ times duplication [i] based on digital (174, 224, 640)-net over F₃, using
- t-expansion [i] based on digital (173, 224, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 56, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(225−50, 225, 1507)-Net over F₃ — Digital

Digital (175, 225, 1507)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−50, 225, 100133)-Net in Base 3 — Upper bound on s

There is no (175, 225, 100134)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225060 477685 369275 843549 316520 737162 356657 210454 307725 423676 852324 532777 642288 149635 663473 099752 065646 426013 > 3²²⁵ [i]