MinT - Best Known (183−73, 183, s)-Nets in Base 3

Best Known (183−73, 183, s)-Nets in Base 3

(183−73, 183, 148)-Net over F₃ — Constructive and digital

Digital (110, 183, 148)-net over F₃, using

3 times m-reduction [i] based on digital (110, 186, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 93, 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]

(183−73, 183, 174)-Net over F₃ — Digital

Digital (110, 183, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183−73, 183, 1809)-Net in Base 3 — Upper bound on s

There is no (110, 183, 1810)-net in base 3, because

1 times m-reduction [i] would yield (110, 182, 1810)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 698 649547 261520 872364 993670 654179 962487 104057 575183 341900 262733 812348 481915 097567 857257 > 3¹⁸² [i]