MinT - Best Known (186−85, 186, s)-Nets in Base 3

Best Known (186−85, 186, s)-Nets in Base 3

(186−85, 186, 80)-Net over F₃ — Constructive and digital

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]

(186−85, 186, 121)-Net over F₃ — Digital

Digital (101, 186, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−85, 186, 1002)-Net in Base 3 — Upper bound on s

There is no (101, 186, 1003)-net in base 3, because

1 times m-reduction [i] would yield (101, 185, 1003)-net in base 3, but
- 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]