MinT - Best Known (135−49, 135, s)-Nets in Base 3

Best Known (135−49, 135, s)-Nets in Base 3

(135−49, 135, 148)-Net over F₃ — Constructive and digital

Digital (86, 135, 148)-net over F₃, using

3 times m-reduction [i] based on digital (86, 138, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 69, 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]

(135−49, 135, 177)-Net over F₃ — Digital

Digital (86, 135, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−49, 135, 2237)-Net in Base 3 — Upper bound on s

There is no (86, 135, 2238)-net in base 3, because

1 times m-reduction [i] would yield (86, 134, 2238)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8650 962358 613154 509011 329800 462455 569790 103953 065055 688732 153841 > 3¹³⁴ [i]