MinT - Best Known (210−44, 210, s)-Nets in Base 2

Best Known (210−44, 210, s)-Nets in Base 2

(210−44, 210, 260)-Net over F₂ — Constructive and digital

Digital (166, 210, 260)-net over F₂, using

t-expansion [i] based on digital (165, 210, 260)-net over F₂, using
- 2 times m-reduction [i] based on 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]

(210−44, 210, 470)-Net over F₂ — Digital

Digital (166, 210, 470)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−44, 210, 6733)-Net in Base 2 — Upper bound on s

There is no (166, 210, 6734)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1648 705078 164192 365747 996227 727917 523345 086594 778871 726009 937872 > 2²¹⁰ [i]