MinT - Best Known (145, 145+47, s)-Nets in Base 3

Best Known (145, 145+47, s)-Nets in Base 3

(145, 145+47, 400)-Net over F₃ — Constructive and digital

Digital (145, 192, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 48, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(145, 145+47, 895)-Net over F₃ — Digital

Digital (145, 192, 895)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+47, 43189)-Net in Base 3 — Upper bound on s

There is no (145, 192, 43190)-net in base 3, because

1 times m-reduction [i] would yield (145, 191, 43190)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 496164 656263 751775 172572 678585 615193 795497 395687 628762 257800 114000 822968 535662 781396 118969 > 3¹⁹¹ [i]