MinT - Best Known (100, 100+61, s)-Nets in Base 3

Best Known (100, 100+61, s)-Nets in Base 3

(100, 100+61, 148)-Net over F₃ — Constructive and digital

Digital (100, 161, 148)-net over F₃, using

5 times m-reduction [i] based on digital (100, 166, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 83, 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]

(100, 100+61, 181)-Net over F₃ — Digital

Digital (100, 161, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+61, 2081)-Net in Base 3 — Upper bound on s

There is no (100, 161, 2082)-net in base 3, because

1 times m-reduction [i] would yield (100, 160, 2082)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22075 863245 138437 734353 399059 962223 766836 786205 801529 461380 765207 290747 180525 > 3¹⁶⁰ [i]