MinT - Best Known (65, 65+29, s)-Nets in Base 3

Best Known (65, 65+29, s)-Nets in Base 3

(65, 65+29, 148)-Net over F₃ — Constructive and digital

Digital (65, 94, 148)-net over F₃, using

2 times m-reduction [i] based on digital (65, 96, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 48, 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]

(65, 65+29, 220)-Net over F₃ — Digital

Digital (65, 94, 220)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+29, 4452)-Net in Base 3 — Upper bound on s

There is no (65, 94, 4453)-net in base 3, because

1 times m-reduction [i] would yield (65, 93, 4453)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 236 336654 600050 100688 111345 072094 771808 034081 > 3⁹³ [i]