MinT - Best Known (207−53, 207, s)-Nets in Base 2

Best Known (207−53, 207, s)-Nets in Base 2

(207−53, 207, 195)-Net over F₂ — Constructive and digital

Digital (154, 207, 195)-net over F₂, using

3 times m-reduction [i] based on digital (154, 210, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 70, 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]

(207−53, 207, 271)-Net over F₂ — Digital

Digital (154, 207, 271)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−53, 207, 2522)-Net in Base 2 — Upper bound on s

There is no (154, 207, 2523)-net in base 2, because

1 times m-reduction [i] would yield (154, 206, 2523)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103 294564 104129 794933 174466 480474 743150 602462 839485 991180 294473 > 2²⁰⁶ [i]