MinT - Best Known (202−81, 202, s)-Nets in Base 3

Best Known (202−81, 202, s)-Nets in Base 3

(202−81, 202, 148)-Net over F₃ — Constructive and digital

Digital (121, 202, 148)-net over F₃, using

6 times m-reduction [i] based on digital (121, 208, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 104, 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]

(202−81, 202, 187)-Net over F₃ — Digital

Digital (121, 202, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−81, 202, 1930)-Net in Base 3 — Upper bound on s

There is no (121, 202, 1931)-net in base 3, because

1 times m-reduction [i] would yield (121, 201, 1931)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 812323 978425 103789 252179 095971 561130 291208 715431 932505 850539 438956 687666 538117 315110 117882 595377 > 3²⁰¹ [i]