MinT - Best Known (148, 148+87, s)-Nets in Base 3

Best Known (148, 148+87, s)-Nets in Base 3

(148, 148+87, 156)-Net over F₃ — Constructive and digital

Digital (148, 235, 156)-net over F₃, using

t-expansion [i] based on digital (147, 235, 156)-net over F₃, using
- 15 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+87, 269)-Net over F₃ — Digital

Digital (148, 235, 269)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+87, 3290)-Net in Base 3 — Upper bound on s

There is no (148, 235, 3291)-net in base 3, because

1 times m-reduction [i] would yield (148, 234, 3291)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4432 047776 208414 371017 105106 412700 189738 258243 138955 303514 472312 492210 942179 110370 862633 775211 611632 519458 662715 > 3²³⁴ [i]