MinT - Best Known (209−55, 209, s)-Nets in Base 3

Best Known (209−55, 209, s)-Nets in Base 3

(209−55, 209, 288)-Net over F₃ — Constructive and digital

Digital (154, 209, 288)-net over F₃, using

t-expansion [i] based on digital (153, 209, 288)-net over F₃, using
- 4 times m-reduction [i] based on digital (153, 213, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 71, 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]

(209−55, 209, 724)-Net over F₃ — Digital

Digital (154, 209, 724)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−55, 209, 25854)-Net in Base 3 — Upper bound on s

There is no (154, 209, 25855)-net in base 3, because

1 times m-reduction [i] would yield (154, 208, 25855)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1743 961583 056663 772439 815529 839913 129932 035948 676424 197895 740238 628136 331939 670957 639511 757948 990411 > 3²⁰⁸ [i]