MinT - Best Known (135−60, 135, s)-Nets in Base 3

Best Known (135−60, 135, s)-Nets in Base 3

(135−60, 135, 72)-Net over F₃ — Constructive and digital

Digital (75, 135, 72)-net over F₃, using

1 times m-reduction [i] based on digital (75, 136, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 68, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(135−60, 135, 100)-Net over F₃ — Digital

Digital (75, 135, 100)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−60, 135, 815)-Net in Base 3 — Upper bound on s

There is no (75, 135, 816)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25950 253094 910967 582684 666668 671055 382616 144943 513547 516473 200673 > 3¹³⁵ [i]