MinT - Best Known (102−33, 102, s)-Nets in Base 3

Best Known (102−33, 102, s)-Nets in Base 3

(102−33, 102, 148)-Net over F₃ — Constructive and digital

Digital (69, 102, 148)-net over F₃, using

2 times m-reduction [i] based on digital (69, 104, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 52, 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]

(102−33, 102, 200)-Net over F₃ — Digital

Digital (69, 102, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−33, 102, 3478)-Net in Base 3 — Upper bound on s

There is no (69, 102, 3479)-net in base 3, because

1 times m-reduction [i] would yield (69, 101, 3479)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 548687 991356 970958 558108 795118 723183 652817 161953 > 3¹⁰¹ [i]