MinT - Best Known (172, 172+66, s)-Nets in Base 3

Best Known (172, 172+66, s)-Nets in Base 3

(172, 172+66, 288)-Net over F₃ — Constructive and digital

Digital (172, 238, 288)-net over F₃, using

t-expansion [i] based on digital (171, 238, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 80, 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]

(172, 172+66, 670)-Net over F₃ — Digital

Digital (172, 238, 670)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+66, 18138)-Net in Base 3 — Upper bound on s

There is no (172, 238, 18139)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 359071 323502 580333 301362 474354 744763 812518 198771 356766 384694 723409 641758 486031 266079 401560 720156 932781 438873 704055 > 3²³⁸ [i]