MinT - Best Known (148, 148+101, s)-Nets in Base 3

Best Known (148, 148+101, s)-Nets in Base 3

(148, 148+101, 156)-Net over F₃ — Constructive and digital

Digital (148, 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]

(148, 148+101, 218)-Net over F₃ — Digital

Digital (148, 249, 218)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+101, 2216)-Net in Base 3 — Upper bound on s

There is no (148, 249, 2217)-net in base 3, because

1 times m-reduction [i] would yield (148, 248, 2217)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21475 322895 610330 410109 365809 358812 928221 529374 537233 211376 338989 004914 021018 606265 763328 963572 391257 725820 565241 081817 > 3²⁴⁸ [i]