MinT - Best Known (249−88, 249, s)-Nets in Base 3

Best Known (249−88, 249, s)-Nets in Base 3

(249−88, 249, 162)-Net over F₃ — Constructive and digital

Digital (161, 249, 162)-net over F₃, using

t-expansion [i] based on digital (157, 249, 162)-net over F₃, using
- 1 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
  - trace code for nets [i] based on digital (32, 125, 81)-net over F₉, using
    - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
        F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(249−88, 249, 323)-Net over F₃ — Digital

Digital (161, 249, 323)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−88, 249, 4281)-Net in Base 3 — Upper bound on s

There is no (161, 249, 4282)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63902 228004 781891 387486 665977 609054 788289 834135 210437 563116 565780 000554 431518 431221 934692 275016 478592 694867 696912 610745 > 3²⁴⁹ [i]