MinT - Best Known (198−47, 198, s)-Nets in Base 3

Best Known (198−47, 198, s)-Nets in Base 3

(198−47, 198, 464)-Net over F₃ — Constructive and digital

Digital (151, 198, 464)-net over F₃, using

3² times duplication [i] based on digital (149, 196, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 49, 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]

(198−47, 198, 1041)-Net over F₃ — Digital

Digital (151, 198, 1041)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−47, 198, 57531)-Net in Base 3 — Upper bound on s

There is no (151, 198, 57532)-net in base 3, because

1 times m-reduction [i] would yield (151, 197, 57532)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9840 527900 182185 333153 113689 670140 535328 938306 276784 646546 858703 027665 888599 264381 617091 159057 > 3¹⁹⁷ [i]