MinT - Best Known (101, 101+59, s)-Nets in Base 3

Best Known (101, 101+59, s)-Nets in Base 3

(101, 101+59, 148)-Net over F₃ — Constructive and digital

Digital (101, 160, 148)-net over F₃, using

8 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]

(101, 101+59, 195)-Net over F₃ — Digital

Digital (101, 160, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+59, 2381)-Net in Base 3 — Upper bound on s

There is no (101, 160, 2382)-net in base 3, because

1 times m-reduction [i] would yield (101, 159, 2382)-net in base 3, but
- 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]