MinT - Best Known (161, 161+40, s)-Nets in Base 2

Best Known (161, 161+40, s)-Nets in Base 2

(161, 161+40, 260)-Net over F₂ — Constructive and digital

Digital (161, 201, 260)-net over F₂, using

t-expansion [i] based on digital (159, 201, 260)-net over F₂, using
- 3 times m-reduction [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]

(161, 161+40, 530)-Net over F₂ — Digital

Digital (161, 201, 530)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+40, 8774)-Net in Base 2 — Upper bound on s

There is no (161, 201, 8775)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 220512 463865 397168 030304 362390 757318 906651 924143 780888 834196 > 2²⁰¹ [i]