MinT - Best Known (165−64, 165, s)-Nets in Base 3

Best Known (165−64, 165, s)-Nets in Base 3

(165−64, 165, 148)-Net over F₃ — Constructive and digital

Digital (101, 165, 148)-net over F₃, using

3 times m-reduction [i] based on digital (101, 168, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 84, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(165−64, 165, 173)-Net over F₃ — Digital

Digital (101, 165, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−64, 165, 1813)-Net in Base 3 — Upper bound on s

There is no (101, 165, 1814)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 330423 690026 463159 165306 839231 394330 907908 830401 772265 184092 031168 976490 345793 > 3¹⁶⁵ [i]