MinT - Best Known (160, 160+45, s)-Nets in Base 2

Best Known (160, 160+45, s)-Nets in Base 2

(160, 160+45, 260)-Net over F₂ — Constructive and digital

Digital (160, 205, 260)-net over F₂, using

2¹ times duplication [i] based on digital (159, 204, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 51, 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]

(160, 160+45, 403)-Net over F₂ — Digital

Digital (160, 205, 403)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+45, 5568)-Net in Base 2 — Upper bound on s

There is no (160, 205, 5569)-net in base 2, because

1 times m-reduction [i] would yield (160, 204, 5569)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 809677 603101 635661 182068 448710 752878 288900 646812 550035 835808 > 2²⁰⁴ [i]