MinT - Best Known (210−85, 210, s)-Nets in Base 2

Best Known (210−85, 210, s)-Nets in Base 2

(210−85, 210, 66)-Net over F₂ — Constructive and digital

Digital (125, 210, 66)-net over F₂, using

10 times m-reduction [i] based on digital (125, 220, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 110, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(210−85, 210, 94)-Net over F₂ — Digital

Digital (125, 210, 94)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−85, 210, 460)-Net in Base 2 — Upper bound on s

There is no (125, 210, 461)-net in base 2, because

1 times m-reduction [i] would yield (125, 209, 461)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 859 299499 843978 970236 213990 668254 933697 723422 362039 386511 821980 > 2²⁰⁹ [i]