MinT - Best Known (242−95, 242, s)-Nets in Base 3

Best Known (242−95, 242, s)-Nets in Base 3

(242−95, 242, 156)-Net over F₃ — Constructive and digital

Digital (147, 242, 156)-net over F₃, using

8 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]

(242−95, 242, 233)-Net over F₃ — Digital

Digital (147, 242, 233)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−95, 242, 2521)-Net in Base 3 — Upper bound on s

There is no (147, 242, 2522)-net in base 3, because

1 times m-reduction [i] would yield (147, 241, 2522)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 725616 435567 095121 614923 669876 281844 417469 352502 000908 101974 111797 154034 936779 168852 836814 985081 138330 595836 540793 > 3²⁴¹ [i]