MinT - Best Known (199, 199+52, s)-Nets in Base 2

Best Known (199, 199+52, s)-Nets in Base 2

(199, 199+52, 260)-Net over F₂ — Constructive and digital

Digital (199, 251, 260)-net over F₂, using

t-expansion [i] based on digital (198, 251, 260)-net over F₂, using
- 5 times m-reduction [i] based on digital (198, 256, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 64, 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]

(199, 199+52, 564)-Net over F₂ — Digital

Digital (199, 251, 564)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(199, 199+52, 8461)-Net in Base 2 — Upper bound on s

There is no (199, 251, 8462)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3629 372568 469239 154469 672545 147095 172835 314100 576819 772504 608579 077793 572960 > 2²⁵¹ [i]