MinT - Best Known (97, 97+56, s)-Nets in Base 3

Best Known (97, 97+56, s)-Nets in Base 3

(97, 97+56, 148)-Net over F₃ — Constructive and digital

Digital (97, 153, 148)-net over F₃, using

7 times m-reduction [i] based on digital (97, 160, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 80, 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]

(97, 97+56, 192)-Net over F₃ — Digital

Digital (97, 153, 192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+56, 2258)-Net in Base 3 — Upper bound on s

There is no (97, 153, 2259)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 017570 376222 243405 675886 438242 730549 001819 601907 599304 748061 244924 635945 > 3¹⁵³ [i]