MinT - Best Known (107, 165, s)-Nets in Base 3

Best Known (107, 165, s)-Nets in Base 3

(107, 165, 156)-Net over F₃ — Constructive and digital

Digital (107, 165, 156)-net over F₃, using

5 times m-reduction [i] based on digital (107, 170, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 85, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(107, 165, 230)-Net over F₃ — Digital

Digital (107, 165, 230)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 165, 2996)-Net in Base 3 — Upper bound on s

There is no (107, 165, 2997)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 320885 825856 366920 884261 732625 582060 083372 259858 681218 398153 355559 155847 870747 > 3¹⁶⁵ [i]