MinT - Best Known (73, 73+41, s)-Nets in Base 3

Best Known (73, 73+41, s)-Nets in Base 3

(73, 73+41, 128)-Net over F₃ — Constructive and digital

Digital (73, 114, 128)-net over F₃, using

6 times m-reduction [i] based on digital (73, 120, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 60, 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]

(73, 73+41, 159)-Net over F₃ — Digital

Digital (73, 114, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+41, 2041)-Net in Base 3 — Upper bound on s

There is no (73, 114, 2042)-net in base 3, because

1 times m-reduction [i] would yield (73, 113, 2042)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 827596 251698 360326 597482 188393 606399 910435 160643 505993 > 3¹¹³ [i]