MinT - Best Known (65, 65+55, s)-Nets in Base 3

Best Known (65, 65+55, s)-Nets in Base 3

(65, 65+55, 64)-Net over F₃ — Constructive and digital

Digital (65, 120, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 60, 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]

(65, 65+55, 83)-Net over F₃ — Digital

Digital (65, 120, 83)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+55, 666)-Net in Base 3 — Upper bound on s

There is no (65, 120, 667)-net in base 3, because

1 times m-reduction [i] would yield (65, 119, 667)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 619 535718 788019 083554 027655 859537 554854 333312 226290 966875 > 3¹¹⁹ [i]