MinT - Best Known (66, 66+55, s)-Nets in Base 3

Best Known (66, 66+55, s)-Nets in Base 3

(66, 66+55, 64)-Net over F₃ — Constructive and digital

Digital (66, 121, 64)-net over F₃, using

1 times m-reduction [i] based on digital (66, 122, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 61, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]

(66, 66+55, 86)-Net over F₃ — Digital

Digital (66, 121, 86)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+55, 694)-Net in Base 3 — Upper bound on s

There is no (66, 121, 695)-net in base 3, because

1 times m-reduction [i] would yield (66, 120, 695)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1806 017880 995186 716744 011608 550650 177885 973326 375042 059307 > 3¹²⁰ [i]