MinT - Best Known (168, 168+64, s)-Nets in Base 3

Best Known (168, 168+64, s)-Nets in Base 3

(168, 168+64, 288)-Net over F₃ — Constructive and digital

Digital (168, 232, 288)-net over F₃, using

t-expansion [i] based on digital (167, 232, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (167, 234, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 78, 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]

(168, 168+64, 667)-Net over F₃ — Digital

Digital (168, 232, 667)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+64, 18375)-Net in Base 3 — Upper bound on s

There is no (168, 232, 18376)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 725475 773404 251664 193117 363030 156765 917379 337590 270755 502774 668104 931011 870541 247236 785187 191326 438712 135681 > 3²³² [i]