MinT - Best Known (131, 131+70, s)-Nets in Base 3

Best Known (131, 131+70, s)-Nets in Base 3

(131, 131+70, 156)-Net over F₃ — Constructive and digital

Digital (131, 201, 156)-net over F₃, using

17 times m-reduction [i] based on digital (131, 218, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 109, 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]

(131, 131+70, 280)-Net over F₃ — Digital

Digital (131, 201, 280)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+70, 3787)-Net in Base 3 — Upper bound on s

There is no (131, 201, 3788)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 800690 779887 189642 533978 774937 931450 445599 294931 179170 448972 464197 835413 668300 162271 481996 159825 > 3²⁰¹ [i]