MinT - Best Known (251−69, 251, s)-Nets in Base 2

Best Known (251−69, 251, s)-Nets in Base 2

(251−69, 251, 195)-Net over F₂ — Constructive and digital

Digital (182, 251, 195)-net over F₂, using

1 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 84, 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]

(251−69, 251, 267)-Net over F₂ — Digital

Digital (182, 251, 267)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−69, 251, 2162)-Net in Base 2 — Upper bound on s

There is no (182, 251, 2163)-net in base 2, because

1 times m-reduction [i] would yield (182, 250, 2163)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1815 764041 092203 132108 567836 078382 875546 071619 789270 589014 222787 455993 291693 > 2²⁵⁰ [i]