MinT - Best Known (201−81, 201, s)-Nets in Base 2

Best Known (201−81, 201, s)-Nets in Base 2

(201−81, 201, 66)-Net over F₂ — Constructive and digital

Digital (120, 201, 66)-net over F₂, using

9 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]

(201−81, 201, 91)-Net over F₂ — Digital

Digital (120, 201, 91)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−81, 201, 448)-Net in Base 2 — Upper bound on s

There is no (120, 201, 449)-net in base 2, because

1 times m-reduction [i] would yield (120, 200, 449)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 725217 266832 187179 015597 850371 323846 808296 720779 225781 249624 > 2²⁰⁰ [i]