MinT - Best Known (240−92, 240, s)-Nets in Base 3

Best Known (240−92, 240, s)-Nets in Base 3

(240−92, 240, 156)-Net over F₃ — Constructive and digital

Digital (148, 240, 156)-net over F₃, using

t-expansion [i] based on digital (147, 240, 156)-net over F₃, using
- 10 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 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]

(240−92, 240, 247)-Net over F₃ — Digital

Digital (148, 240, 247)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−92, 240, 2731)-Net in Base 3 — Upper bound on s

There is no (148, 240, 2732)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 255962 165510 199697 883376 780831 539932 658133 204503 844929 340288 287824 297785 178380 044892 043455 384468 083834 421261 059145 > 3²⁴⁰ [i]