MinT - Best Known (206−54, 206, s)-Nets in Base 2

Best Known (206−54, 206, s)-Nets in Base 2

(206−54, 206, 195)-Net over F₂ — Constructive and digital

Digital (152, 206, 195)-net over F₂, using

1 times m-reduction [i] based on digital (152, 207, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 69, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(206−54, 206, 254)-Net over F₂ — Digital

Digital (152, 206, 254)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−54, 206, 2123)-Net in Base 2 — Upper bound on s

There is no (152, 206, 2124)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103 073944 171271 835117 801857 897041 831460 524318 653118 380883 524764 > 2²⁰⁶ [i]