MinT - Best Known (194−82, 194, s)-Nets in Base 3

Best Known (194−82, 194, s)-Nets in Base 3

(194−82, 194, 128)-Net over F₃ — Constructive and digital

Digital (112, 194, 128)-net over F₃, using

4 times m-reduction [i] based on digital (112, 198, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 99, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(194−82, 194, 156)-Net over F₃ — Digital

Digital (112, 194, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−82, 194, 1420)-Net in Base 3 — Upper bound on s

There is no (112, 194, 1421)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370 619553 937648 409700 386718 129112 532631 426578 635726 454287 733013 609874 628519 275390 831477 473915 > 3¹⁹⁴ [i]