MinT - Best Known (240−91, 240, s)-Nets in Base 3

Best Known (240−91, 240, s)-Nets in Base 3

(240−91, 240, 156)-Net over F₃ — Constructive and digital

Digital (149, 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]

(240−91, 240, 255)-Net over F₃ — Digital

Digital (149, 240, 255)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−91, 240, 2970)-Net in Base 3 — Upper bound on s

There is no (149, 240, 2971)-net in base 3, because

1 times m-reduction [i] would yield (149, 239, 2971)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 091303 629252 190239 778824 299064 807375 102179 004121 631928 959031 656547 534739 141050 178794 117000 511115 104191 241833 024479 > 3²³⁹ [i]