MinT - Best Known (161−58, 161, s)-Nets in Base 3

Best Known (161−58, 161, s)-Nets in Base 3

(161−58, 161, 156)-Net over F₃ — Constructive and digital

Digital (103, 161, 156)-net over F₃, using

1 times m-reduction [i] based on digital (103, 162, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 81, 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]

(161−58, 161, 209)-Net over F₃ — Digital

Digital (103, 161, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−58, 161, 2571)-Net in Base 3 — Upper bound on s

There is no (103, 161, 2572)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65970 761648 016094 804490 338874 420472 178121 046829 588739 220962 633846 923206 643449 > 3¹⁶¹ [i]