MinT - Best Known (239−63, 239, s)-Nets in Base 3

Best Known (239−63, 239, s)-Nets in Base 3

(239−63, 239, 288)-Net over F₃ — Constructive and digital

Digital (176, 239, 288)-net over F₃, using

t-expansion [i] based on digital (175, 239, 288)-net over F₃, using
- 7 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 82, 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]

(239−63, 239, 806)-Net over F₃ — Digital

Digital (176, 239, 806)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−63, 239, 28549)-Net in Base 3 — Upper bound on s

There is no (176, 239, 28550)-net in base 3, because

1 times m-reduction [i] would yield (176, 238, 28550)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 358976 636068 145558 936657 971724 440973 656748 295166 837721 328720 246602 860863 961257 641912 567169 396760 839278 455325 246505 > 3²³⁸ [i]