MinT - Best Known (165, 165+47, s)-Nets in Base 2

Best Known (165, 165+47, s)-Nets in Base 2

(165, 165+47, 260)-Net over F₂ — Constructive and digital

Digital (165, 212, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 53, 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]

(165, 165+47, 404)-Net over F₂ — Digital

Digital (165, 212, 404)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+47, 5412)-Net in Base 2 — Upper bound on s

There is no (165, 212, 5413)-net in base 2, because

1 times m-reduction [i] would yield (165, 211, 5413)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3303 300567 679171 594477 257675 508184 855386 664245 344590 203474 786512 > 2²¹¹ [i]