MinT - Best Known (192, 192+53, s)-Nets in Base 2

Best Known (192, 192+53, s)-Nets in Base 2

(192, 192+53, 260)-Net over F₂ — Constructive and digital

Digital (192, 245, 260)-net over F₂, using

3 times m-reduction [i] based on digital (192, 248, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 62, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(192, 192+53, 489)-Net over F₂ — Digital

Digital (192, 245, 489)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(192, 192+53, 7014)-Net in Base 2 — Upper bound on s

There is no (192, 245, 7015)-net in base 2, because

1 times m-reduction [i] would yield (192, 244, 7015)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 362793 307726 367358 944765 914917 581770 680663 891473 159466 376123 404276 779332 > 2²⁴⁴ [i]