MinT - Best Known (247−88, 247, s)-Nets in Base 3

Best Known (247−88, 247, s)-Nets in Base 3

(247−88, 247, 162)-Net over F₃ — Constructive and digital

Digital (159, 247, 162)-net over F₃, using

t-expansion [i] based on digital (157, 247, 162)-net over F₃, using
- 3 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]

(247−88, 247, 314)-Net over F₃ — Digital

Digital (159, 247, 314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−88, 247, 4070)-Net in Base 3 — Upper bound on s

There is no (159, 247, 4071)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7075 951753 275467 294852 788990 612530 362730 042810 317248 346094 953575 816242 278696 459269 741596 790842 732699 192857 200378 147497 > 3²⁴⁷ [i]