MinT - Best Known (136, 136+47, s)-Nets in Base 3

Best Known (136, 136+47, s)-Nets in Base 3

(136, 136+47, 288)-Net over F₃ — Constructive and digital

Digital (136, 183, 288)-net over F₃, using

t-expansion [i] based on digital (135, 183, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (135, 186, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 62, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(136, 136+47, 711)-Net over F₃ — Digital

Digital (136, 183, 711)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+47, 28090)-Net in Base 3 — Upper bound on s

There is no (136, 183, 28091)-net in base 3, because

1 times m-reduction [i] would yield (136, 182, 28091)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 685 860637 916823 356151 651751 924292 102198 001715 880213 847834 500819 559719 304968 796585 392451 > 3¹⁸² [i]