MinT - Best Known (69, 69+35, s)-Nets in Base 3

Best Known (69, 69+35, s)-Nets in Base 3

(69, 69+35, 148)-Net over F₃ — Constructive and digital

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]

(69, 69+35, 180)-Net over F₃ — Digital

Digital (69, 104, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+35, 2774)-Net in Base 3 — Upper bound on s

There is no (69, 104, 2775)-net in base 3, because

1 times m-reduction [i] would yield (69, 103, 2775)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 982134 985688 774072 117510 829651 126296 756009 134991 > 3¹⁰³ [i]