MinT - Best Known (134, 227, s)-Nets in Base 3

Best Known (134, 227, s)-Nets in Base 3

(134, 227, 148)-Net over F₃ — Constructive and digital

Digital (134, 227, 148)-net over F₃, using

7 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]

(134, 227, 195)-Net over F₃ — Digital

Digital (134, 227, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 227, 1942)-Net in Base 3 — Upper bound on s

There is no (134, 227, 1943)-net in base 3, because

1 times m-reduction [i] would yield (134, 226, 1943)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 683400 957880 956574 943280 143405 415860 948651 836151 890157 175314 910166 740929 764409 617584 532513 929863 420300 796437 > 3²²⁶ [i]