MinT - Best Known (249−102, 249, s)-Nets in Base 3

Best Known (249−102, 249, s)-Nets in Base 3

(249−102, 249, 156)-Net over F₃ — Constructive and digital

Digital (147, 249, 156)-net over F₃, using

1 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 125, 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]

(249−102, 249, 212)-Net over F₃ — Digital

Digital (147, 249, 212)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−102, 249, 2069)-Net in Base 3 — Upper bound on s

There is no (147, 249, 2070)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63835 461190 686477 660825 371549 694622 853715 648613 749239 654917 392757 853202 220754 756836 418440 419018 595425 479650 899833 057217 > 3²⁴⁹ [i]