MinT - Best Known (210−42, 210, s)-Nets in Base 2

Best Known (210−42, 210, s)-Nets in Base 2

(210−42, 210, 260)-Net over F₂ — Constructive and digital

Digital (168, 210, 260)-net over F₂, using

6 times m-reduction [i] based on digital (168, 216, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 54, 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]

(210−42, 210, 541)-Net over F₂ — Digital

Digital (168, 210, 541)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−42, 210, 8856)-Net in Base 2 — Upper bound on s

There is no (168, 210, 8857)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1646 230145 271093 144265 340443 306225 338196 311567 745994 731211 966204 > 2²¹⁰ [i]