MinT - Best Known (117, 117+59, s)-Nets in Base 3

Best Known (117, 117+59, s)-Nets in Base 3

(117, 117+59, 156)-Net over F₃ — Constructive and digital

Digital (117, 176, 156)-net over F₃, using

14 times m-reduction [i] based on digital (117, 190, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 95, 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]

(117, 117+59, 281)-Net over F₃ — Digital

Digital (117, 176, 281)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+59, 4390)-Net in Base 3 — Upper bound on s

There is no (117, 176, 4391)-net in base 3, because

1 times m-reduction [i] would yield (117, 175, 4391)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 315452 473276 871807 163017 140976 786710 713616 010603 871890 645956 810764 714241 607016 761943 > 3¹⁷⁵ [i]