MinT - Best Known (175, 226, s)-Nets in Base 3

Best Known (175, 226, s)-Nets in Base 3

(175, 226, 640)-Net over F₃ — Constructive and digital

Digital (175, 226, 640)-net over F₃, using

3² times duplication [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]

(175, 226, 1422)-Net over F₃ — Digital

Digital (175, 226, 1422)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 226, 100133)-Net in Base 3 — Upper bound on s

There is no (175, 226, 100134)-net in base 3, because

1 times m-reduction [i] would yield (175, 225, 100134)-net in base 3, but
- 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]