MinT - Best Known (134, 229, s)-Nets in Base 3

Best Known (134, 229, s)-Nets in Base 3

(134, 229, 148)-Net over F₃ — Constructive and digital

Digital (134, 229, 148)-net over F₃, using

5 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, 229, 190)-Net over F₃ — Digital

Digital (134, 229, 190)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 229, 1848)-Net in Base 3 — Upper bound on s

There is no (134, 229, 1849)-net in base 3, because

1 times m-reduction [i] would yield (134, 228, 1849)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 077164 445622 143462 069796 051388 057393 907999 167283 636965 413438 745890 767616 688457 146181 473746 863606 344856 473803 > 3²²⁸ [i]