MinT - Best Known (102, 171, s)-Nets in Base 3

Best Known (102, 171, s)-Nets in Base 3

(102, 171, 128)-Net over F₃ — Constructive and digital

Digital (102, 171, 128)-net over F₃, using

7 times m-reduction [i] based on digital (102, 178, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 89, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(102, 171, 159)-Net over F₃ — Digital

Digital (102, 171, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 171, 1611)-Net in Base 3 — Upper bound on s

There is no (102, 171, 1612)-net in base 3, because

1 times m-reduction [i] would yield (102, 170, 1612)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1307 539914 814864 679769 468012 998761 043236 687392 806647 343697 338948 258057 050368 372969 > 3¹⁷⁰ [i]