MinT - Best Known (65, 65+57, s)-Nets in Base 3

Best Known (65, 65+57, s)-Nets in Base 3

(65, 65+57, 60)-Net over F₃ — Constructive and digital

Digital (65, 122, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 61, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]

(65, 65+57, 80)-Net over F₃ — Digital

Digital (65, 122, 80)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+57, 624)-Net in Base 3 — Upper bound on s

There is no (65, 122, 625)-net in base 3, because

1 times m-reduction [i] would yield (65, 121, 625)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5547 812503 015042 027537 468842 972950 836916 115308 348697 690801 > 3¹²¹ [i]