MinT - Best Known (145, 145+100, s)-Nets in Base 3

Best Known (145, 145+100, s)-Nets in Base 3

(145, 145+100, 156)-Net over F₃ — Constructive and digital

Digital (145, 245, 156)-net over F₃, using

1 times m-reduction [i] based on digital (145, 246, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 123, 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, 145+100, 211)-Net over F₃ — Digital

Digital (145, 245, 211)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+100, 2071)-Net in Base 3 — Upper bound on s

There is no (145, 245, 2072)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 786 512084 451238 192730 031227 904776 065689 305593 119399 922586 759764 740517 482009 713843 532999 277511 304255 694078 989244 879377 > 3²⁴⁵ [i]