MinT - Best Known (137−47, 137, s)-Nets in Base 3

Best Known (137−47, 137, s)-Nets in Base 3

(137−47, 137, 148)-Net over F₃ — Constructive and digital

Digital (90, 137, 148)-net over F₃, using

9 times m-reduction [i] based on digital (90, 146, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 73, 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]

(137−47, 137, 213)-Net over F₃ — Digital

Digital (90, 137, 213)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−47, 137, 3101)-Net in Base 3 — Upper bound on s

There is no (90, 137, 3102)-net in base 3, because

1 times m-reduction [i] would yield (90, 136, 3102)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77791 444880 394542 790497 298456 161580 511812 895662 711619 204909 294361 > 3¹³⁶ [i]