MinT - Best Known (209−56, 209, s)-Nets in Base 2

Best Known (209−56, 209, s)-Nets in Base 2

(209−56, 209, 144)-Net over F₂ — Constructive and digital

Digital (153, 209, 144)-net over F₂, using

4 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]

(209−56, 209, 243)-Net over F₂ — Digital

Digital (153, 209, 243)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−56, 209, 1954)-Net in Base 2 — Upper bound on s

There is no (153, 209, 1955)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 833 725020 022002 422073 918611 879075 974850 086062 331668 247006 370760 > 2²⁰⁹ [i]