MinT - Best Known (190−45, 190, s)-Nets in Base 3

Best Known (190−45, 190, s)-Nets in Base 3

(190−45, 190, 464)-Net over F₃ — Constructive and digital

Digital (145, 190, 464)-net over F₃, using

3² times duplication [i] based on digital (143, 188, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 47, 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]

(190−45, 190, 1013)-Net over F₃ — Digital

Digital (145, 190, 1013)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−45, 190, 56828)-Net in Base 3 — Upper bound on s

There is no (145, 190, 56829)-net in base 3, because

1 times m-reduction [i] would yield (145, 189, 56829)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 499847 457177 719703 294303 911015 021840 884753 902596 758372 832734 030805 381999 778320 520751 810097 > 3¹⁸⁹ [i]