MinT - Best Known (74, 74+47, s)-Nets in Base 3

Best Known (74, 74+47, s)-Nets in Base 3

(74, 74+47, 128)-Net over F₃ — Constructive and digital

Digital (74, 121, 128)-net over F₃, using

1 times m-reduction [i] based on digital (74, 122, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 61, 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]

(74, 74+47, 133)-Net over F₃ — Digital

Digital (74, 121, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+47, 1432)-Net in Base 3 — Upper bound on s

There is no (74, 121, 1433)-net in base 3, because

1 times m-reduction [i] would yield (74, 120, 1433)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1817 549370 676698 545807 996107 053882 206585 178849 797941 614507 > 3¹²⁰ [i]