MinT - Best Known (148, 148+89, s)-Nets in Base 3

Best Known (148, 148+89, s)-Nets in Base 3

(148, 148+89, 156)-Net over F₃ — Constructive and digital

Digital (148, 237, 156)-net over F₃, using

t-expansion [i] based on digital (147, 237, 156)-net over F₃, using
- 13 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+89, 260)-Net over F₃ — Digital

Digital (148, 237, 260)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+89, 3082)-Net in Base 3 — Upper bound on s

There is no (148, 237, 3083)-net in base 3, because

1 times m-reduction [i] would yield (148, 236, 3083)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39972 285863 445657 112855 813795 581242 883830 715966 989371 909886 950013 640223 409620 178622 575381 449376 128709 419640 495241 > 3²³⁶ [i]