MinT - Best Known (247−66, 247, s)-Nets in Base 3

Best Known (247−66, 247, s)-Nets in Base 3

(247−66, 247, 288)-Net over F₃ — Constructive and digital

Digital (181, 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]

(247−66, 247, 789)-Net over F₃ — Digital

Digital (181, 247, 789)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−66, 247, 24486)-Net in Base 3 — Upper bound on s

There is no (181, 247, 24487)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7066 051228 748332 863607 914362 231542 069323 277271 502571 394852 290499 791013 896624 398744 357348 728460 588151 969121 768046 097167 > 3²⁴⁷ [i]