MinT - Best Known (252−51, 252, s)-Nets in Base 2

Best Known (252−51, 252, s)-Nets in Base 2

(252−51, 252, 260)-Net over F₂ — Constructive and digital

Digital (201, 252, 260)-net over F₂, using

8 times m-reduction [i] based on digital (201, 260, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 65, 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]

(252−51, 252, 607)-Net over F₂ — Digital

Digital (201, 252, 607)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−51, 252, 10677)-Net in Base 2 — Upper bound on s

There is no (201, 252, 10678)-net in base 2, because

1 times m-reduction [i] would yield (201, 251, 10678)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3623 261067 946874 666535 929504 013921 979048 730806 758204 464241 294337 766232 752684 > 2²⁵¹ [i]