MinT - Best Known (231−97, 231, s)-Nets in Base 3

Best Known (231−97, 231, s)-Nets in Base 3

(231−97, 231, 148)-Net over F₃ — Constructive and digital

Digital (134, 231, 148)-net over F₃, using

3 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]

(231−97, 231, 185)-Net over F₃ — Digital

Digital (134, 231, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−97, 231, 1764)-Net in Base 3 — Upper bound on s

There is no (134, 231, 1765)-net in base 3, because

1 times m-reduction [i] would yield (134, 230, 1765)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55 845032 958672 121863 078204 713268 554370 048352 313259 542422 364103 092613 588516 084380 179249 279588 437942 923642 705217 > 3²³⁰ [i]