MinT - Best Known (206−57, 206, s)-Nets in Base 2

Best Known (206−57, 206, s)-Nets in Base 2

(206−57, 206, 144)-Net over F₂ — Constructive and digital

Digital (149, 206, 144)-net over F₂, using

1 times m-reduction [i] based on digital (149, 207, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 69, 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]

(206−57, 206, 222)-Net over F₂ — Digital

Digital (149, 206, 222)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−57, 206, 1765)-Net in Base 2 — Upper bound on s

There is no (149, 206, 1766)-net in base 2, because

1 times m-reduction [i] would yield (149, 205, 1766)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 51 422710 129170 810058 455021 265233 042316 684984 743416 469088 890156 > 2²⁰⁵ [i]