MinT - Best Known (231−95, 231, s)-Nets in Base 3

Best Known (231−95, 231, s)-Nets in Base 3

(231−95, 231, 148)-Net over F₃ — Constructive and digital

Digital (136, 231, 148)-net over F₃, using

7 times m-reduction [i] based on digital (136, 238, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 119, 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]

(231−95, 231, 196)-Net over F₃ — Digital

Digital (136, 231, 196)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−95, 231, 1939)-Net in Base 3 — Upper bound on s

There is no (136, 231, 1940)-net in base 3, because

1 times m-reduction [i] would yield (136, 230, 1940)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55 118302 804556 312844 480216 174556 594376 043728 030311 364447 620827 139438 463388 594037 913170 331791 643802 775762 917873 > 3²³⁰ [i]