MinT - Best Known (247−68, 247, s)-Nets in Base 3

Best Known (247−68, 247, s)-Nets in Base 3

(247−68, 247, 288)-Net over F₃ — Constructive and digital

Digital (179, 247, 288)-net over F₃, using

t-expansion [i] based on digital (177, 247, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 83, 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]

(247−68, 247, 710)-Net over F₃ — Digital

Digital (179, 247, 710)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−68, 247, 19763)-Net in Base 3 — Upper bound on s

There is no (179, 247, 19764)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7072 770348 373860 561504 327662 106727 014150 864924 351721 341184 901505 926675 700818 351678 263070 413564 101129 488880 771040 292953 > 3²⁴⁷ [i]