MinT - Best Known (145−45, 145, s)-Nets in Base 3

Best Known (145−45, 145, s)-Nets in Base 3

(145−45, 145, 156)-Net over F₃ — Constructive and digital

Digital (100, 145, 156)-net over F₃, using

11 times m-reduction [i] based on digital (100, 156, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 78, 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]

(145−45, 145, 303)-Net over F₃ — Digital

Digital (100, 145, 303)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−45, 145, 5987)-Net in Base 3 — Upper bound on s

There is no (100, 145, 5988)-net in base 3, because

1 times m-reduction [i] would yield (100, 144, 5988)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 508 493870 670222 565326 624904 532937 673779 424932 613861 694804 205308 753433 > 3¹⁴⁴ [i]