MinT - Best Known (133−48, 133, s)-Nets in Base 3

Best Known (133−48, 133, s)-Nets in Base 3

(133−48, 133, 148)-Net over F₃ — Constructive and digital

Digital (85, 133, 148)-net over F₃, using

3 times m-reduction [i] based on digital (85, 136, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 68, 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]

(133−48, 133, 178)-Net over F₃ — Digital

Digital (85, 133, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−48, 133, 2136)-Net in Base 3 — Upper bound on s

There is no (85, 133, 2137)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2889 376002 120837 030377 700993 612309 639164 964444 638415 753344 249313 > 3¹³³ [i]