MinT - Best Known (239−68, 239, s)-Nets in Base 3

Best Known (239−68, 239, s)-Nets in Base 3

(239−68, 239, 288)-Net over F₃ — Constructive and digital

Digital (171, 239, 288)-net over F₃, using

1 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]

(239−68, 239, 616)-Net over F₃ — Digital

Digital (171, 239, 616)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−68, 239, 15253)-Net in Base 3 — Upper bound on s

There is no (171, 239, 15254)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 077123 851204 477441 483372 663949 150700 849885 458118 134145 806701 139659 679161 330288 111480 924912 884326 281765 659747 389837 > 3²³⁹ [i]