MinT - Best Known (150, 249, s)-Nets in Base 3

Best Known (150, 249, s)-Nets in Base 3

(150, 249, 156)-Net over F₃ — Constructive and digital

Digital (150, 249, 156)-net over F₃, using

t-expansion [i] based on 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]

(150, 249, 230)-Net over F₃ — Digital

Digital (150, 249, 230)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 249, 2435)-Net in Base 3 — Upper bound on s

There is no (150, 249, 2436)-net in base 3, because

1 times m-reduction [i] would yield (150, 248, 2436)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21366 204336 102108 443946 462462 791037 224742 310806 524105 367092 904364 304938 975504 556066 432738 583380 168919 560845 757660 888073 > 3²⁴⁸ [i]