MinT - Best Known (136, 136+48, s)-Nets in Base 3

Best Known (136, 136+48, s)-Nets in Base 3

(136, 136+48, 288)-Net over F₃ — Constructive and digital

Digital (136, 184, 288)-net over F₃, using

t-expansion [i] based on digital (135, 184, 288)-net over F₃, using
- 2 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+48, 673)-Net over F₃ — Digital

Digital (136, 184, 673)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+48, 22274)-Net in Base 3 — Upper bound on s

There is no (136, 184, 22275)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6174 829545 547841 897863 380226 914614 603628 375295 994626 443426 901045 161552 343242 813431 263441 > 3¹⁸⁴ [i]