MinT - Best Known (197−78, 197, s)-Nets in Base 3

Best Known (197−78, 197, s)-Nets in Base 3

(197−78, 197, 148)-Net over F₃ — Constructive and digital

Digital (119, 197, 148)-net over F₃, using

7 times m-reduction [i] based on digital (119, 204, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 102, 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]

(197−78, 197, 190)-Net over F₃ — Digital

Digital (119, 197, 190)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−78, 197, 1940)-Net in Base 3 — Upper bound on s

There is no (119, 197, 1941)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9853 765977 954138 902380 563601 775353 621384 174424 360874 204849 758122 406164 553748 779262 028949 889179 > 3¹⁹⁷ [i]