MinT - Best Known (210−57, 210, s)-Nets in Base 2

Best Known (210−57, 210, s)-Nets in Base 2

(210−57, 210, 144)-Net over F₂ — Constructive and digital

Digital (153, 210, 144)-net over F₂, using

3 times m-reduction [i] based on digital (153, 213, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 71, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(210−57, 210, 236)-Net over F₂ — Digital

Digital (153, 210, 236)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−57, 210, 1954)-Net in Base 2 — Upper bound on s

There is no (153, 210, 1955)-net in base 2, because

1 times m-reduction [i] would yield (153, 209, 1955)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 833 725020 022002 422073 918611 879075 974850 086062 331668 247006 370760 > 2²⁰⁹ [i]