MinT - Best Known (136, 136+55, s)-Nets in Base 3

Best Known (136, 136+55, s)-Nets in Base 3

(136, 136+55, 252)-Net over F₃ — Constructive and digital

Digital (136, 191, 252)-net over F₃, using

1 times m-reduction [i] based on digital (136, 192, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 64, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(136, 136+55, 487)-Net over F₃ — Digital

Digital (136, 191, 487)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+55, 12415)-Net in Base 3 — Upper bound on s

There is no (136, 191, 12416)-net in base 3, because

1 times m-reduction [i] would yield (136, 190, 12416)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 501024 909411 413294 996006 256491 568036 106052 041132 041939 662218 323188 455021 481150 789978 243585 > 3¹⁹⁰ [i]