MinT - Best Known (220−62, 220, s)-Nets in Base 2

Best Known (220−62, 220, s)-Nets in Base 2

(220−62, 220, 144)-Net over F₂ — Constructive and digital

Digital (158, 220, 144)-net over F₂, using

2¹ times duplication [i] based on digital (157, 219, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 73, 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]

(220−62, 220, 225)-Net over F₂ — Digital

Digital (158, 220, 225)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−62, 220, 1654)-Net in Base 2 — Upper bound on s

There is no (158, 220, 1655)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 707529 212527 764067 551916 608373 630856 823966 883087 877594 826294 394376 > 2²²⁰ [i]