MinT - Best Known (225−91, 225, s)-Nets in Base 3

Best Known (225−91, 225, s)-Nets in Base 3

(225−91, 225, 148)-Net over F₃ — Constructive and digital

Digital (134, 225, 148)-net over F₃, using

9 times m-reduction [i] based on digital (134, 234, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 117, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(225−91, 225, 201)-Net over F₃ — Digital

Digital (134, 225, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−91, 225, 2045)-Net in Base 3 — Upper bound on s

There is no (134, 225, 2046)-net in base 3, because

1 times m-reduction [i] would yield (134, 224, 2046)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75186 817755 733142 974358 958185 684666 953148 008303 008333 898768 732562 162276 584097 834466 451212 623546 429158 809285 > 3²²⁴ [i]