MinT - Best Known (219−60, 219, s)-Nets in Base 2

Best Known (219−60, 219, s)-Nets in Base 2

(219−60, 219, 144)-Net over F₂ — Constructive and digital

Digital (159, 219, 144)-net over F₂, using

3 times m-reduction [i] based on digital (159, 222, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 74, 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]

(219−60, 219, 239)-Net over F₂ — Digital

Digital (159, 219, 239)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−60, 219, 1854)-Net in Base 2 — Upper bound on s

There is no (159, 219, 1855)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 855630 161306 071503 563929 943987 137673 333794 483912 902379 763865 351527 > 2²¹⁹ [i]