MinT - Best Known (159−58, 159, s)-Nets in Base 3

Best Known (159−58, 159, s)-Nets in Base 3

(159−58, 159, 148)-Net over F₃ — Constructive and digital

Digital (101, 159, 148)-net over F₃, using

9 times m-reduction [i] based on digital (101, 168, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 84, 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]

(159−58, 159, 200)-Net over F₃ — Digital

Digital (101, 159, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−58, 159, 2381)-Net in Base 3 — Upper bound on s

There is no (101, 159, 2382)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7306 458484 426444 618214 676172 129616 322133 332833 924013 619841 934201 692975 245061 > 3¹⁵⁹ [i]