MinT - Best Known (160−42, 160, s)-Nets in Base 2

Best Known (160−42, 160, s)-Nets in Base 2

(160−42, 160, 144)-Net over F₂ — Constructive and digital

Digital (118, 160, 144)-net over F₂, using

2¹ times duplication [i] based on digital (117, 159, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 53, 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]

(160−42, 160, 206)-Net over F₂ — Digital

Digital (118, 160, 206)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−42, 160, 1675)-Net in Base 2 — Upper bound on s

There is no (118, 160, 1676)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 469610 172794 114269 750221 871028 653078 082170 567792 > 2¹⁶⁰ [i]