MinT - Best Known (101, 185, s)-Nets in Base 3

Best Known (101, 185, s)-Nets in Base 3

(101, 185, 80)-Net over F₃ — Constructive and digital

Digital (101, 185, 80)-net over F₃, using

1 times m-reduction [i] based on digital (101, 186, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 93, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(101, 185, 122)-Net over F₃ — Digital

Digital (101, 185, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 185, 1002)-Net in Base 3 — Upper bound on s

There is no (101, 185, 1003)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18965 562346 157970 591085 600393 758844 832612 611890 220275 368526 576568 984995 462307 079524 648677 > 3¹⁸⁵ [i]