MinT - Best Known (168−43, 168, s)-Nets in Base 3

Best Known (168−43, 168, s)-Nets in Base 3

(168−43, 168, 288)-Net over F₃ — Constructive and digital

Digital (125, 168, 288)-net over F₃, using

3 times m-reduction [i] based on digital (125, 171, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 57, 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]

(168−43, 168, 674)-Net over F₃ — Digital

Digital (125, 168, 674)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−43, 168, 27001)-Net in Base 3 — Upper bound on s

There is no (125, 168, 27002)-net in base 3, because

1 times m-reduction [i] would yield (125, 167, 27002)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 810120 462197 029642 580609 151482 947856 658873 982090 746065 840854 664525 102418 400045 > 3¹⁶⁷ [i]