MinT - Best Known (165−63, 165, s)-Nets in Base 3

Best Known (165−63, 165, s)-Nets in Base 3

(165−63, 165, 148)-Net over F₃ — Constructive and digital

Digital (102, 165, 148)-net over F₃, using

5 times m-reduction [i] based on digital (102, 170, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 85, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(165−63, 165, 181)-Net over F₃ — Digital

Digital (102, 165, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−63, 165, 2045)-Net in Base 3 — Upper bound on s

There is no (102, 165, 2046)-net in base 3, because

1 times m-reduction [i] would yield (102, 164, 2046)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 790581 594325 856978 525177 984757 565305 842272 317935 401854 650109 026800 711053 960905 > 3¹⁶⁴ [i]