MinT - Best Known (190−44, 190, s)-Nets in Base 3

Best Known (190−44, 190, s)-Nets in Base 3

(190−44, 190, 464)-Net over F₃ — Constructive and digital

Digital (146, 190, 464)-net over F₃, using

2 times m-reduction [i] based on digital (146, 192, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 48, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(190−44, 190, 1104)-Net over F₃ — Digital

Digital (146, 190, 1104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−44, 190, 59739)-Net in Base 3 — Upper bound on s

There is no (146, 190, 59740)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 499513 580549 965900 950567 037192 384169 367135 401255 759213 466661 672525 941072 078477 541677 609449 > 3¹⁹⁰ [i]