MinT - Best Known (205−85, 205, s)-Nets in Base 2

Best Known (205−85, 205, s)-Nets in Base 2

(205−85, 205, 66)-Net over F₂ — Constructive and digital

Digital (120, 205, 66)-net over F₂, using

5 times m-reduction [i] based on digital (120, 210, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 105, 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]

(205−85, 205, 87)-Net over F₂ — Digital

Digital (120, 205, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−85, 205, 419)-Net in Base 2 — Upper bound on s

There is no (120, 205, 420)-net in base 2, because

1 times m-reduction [i] would yield (120, 204, 420)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26 734418 351566 271789 953483 697146 027924 927157 528098 071832 279344 > 2²⁰⁴ [i]