MinT - Best Known (225−53, 225, s)-Nets in Base 2

Best Known (225−53, 225, s)-Nets in Base 2

(225−53, 225, 195)-Net over F₂ — Constructive and digital

Digital (172, 225, 195)-net over F₂, using

12 times m-reduction [i] based on digital (172, 237, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 79, 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]

(225−53, 225, 362)-Net over F₂ — Digital

Digital (172, 225, 362)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−53, 225, 4099)-Net in Base 2 — Upper bound on s

There is no (172, 225, 4100)-net in base 2, because

1 times m-reduction [i] would yield (172, 224, 4100)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 030450 327419 847342 169592 463107 057361 069984 368703 895983 395002 570240 > 2²²⁴ [i]