MinT - Best Known (198−53, 198, s)-Nets in Base 2

Best Known (198−53, 198, s)-Nets in Base 2

(198−53, 198, 144)-Net over F₂ — Constructive and digital

Digital (145, 198, 144)-net over F₂, using

3 times m-reduction [i] based on digital (145, 201, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 67, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(198−53, 198, 233)-Net over F₂ — Digital

Digital (145, 198, 233)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−53, 198, 1976)-Net in Base 2 — Upper bound on s

There is no (145, 198, 1977)-net in base 2, because

1 times m-reduction [i] would yield (145, 197, 1977)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 202520 753487 163246 515217 218648 316190 422523 011813 809693 096908 > 2¹⁹⁷ [i]