MinT - Best Known (196−78, 196, s)-Nets in Base 3

Best Known (196−78, 196, s)-Nets in Base 3

(196−78, 196, 148)-Net over F₃ — Constructive and digital

Digital (118, 196, 148)-net over F₃, using

6 times m-reduction [i] based on digital (118, 202, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 101, 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]

(196−78, 196, 186)-Net over F₃ — Digital

Digital (118, 196, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−78, 196, 1885)-Net in Base 3 — Upper bound on s

There is no (118, 196, 1886)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3282 340030 213035 084826 745369 952828 640142 089414 288805 692556 688854 915810 221114 494369 048367 090041 > 3¹⁹⁶ [i]