MinT - Best Known (69, 69+42, s)-Nets in Base 3

Best Known (69, 69+42, s)-Nets in Base 3

(69, 69+42, 128)-Net over F₃ — Constructive and digital

Digital (69, 111, 128)-net over F₃, using

1 times m-reduction [i] based on digital (69, 112, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 56, 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]

(69, 69+42, 134)-Net over F₃ — Digital

Digital (69, 111, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+42, 1423)-Net in Base 3 — Upper bound on s

There is no (69, 111, 1424)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 92595 905568 591648 025308 514625 770172 714078 022637 514529 > 3¹¹¹ [i]