MinT - Best Known (136−42, 136, s)-Nets in Base 3

Best Known (136−42, 136, s)-Nets in Base 3

(136−42, 136, 156)-Net over F₃ — Constructive and digital

Digital (94, 136, 156)-net over F₃, using

8 times m-reduction [i] based on digital (94, 144, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 72, 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]

(136−42, 136, 292)-Net over F₃ — Digital

Digital (94, 136, 292)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−42, 136, 5317)-Net in Base 3 — Upper bound on s

There is no (94, 136, 5318)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77452 249463 722841 133713 370690 541698 415616 922005 698283 512391 130181 > 3¹³⁶ [i]