MinT - Best Known (163−43, 163, s)-Nets in Base 2

Best Known (163−43, 163, s)-Nets in Base 2

(163−43, 163, 144)-Net over F₂ — Constructive and digital

Digital (120, 163, 144)-net over F₂, using

2¹ times duplication [i] based on digital (119, 162, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 54, 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]

(163−43, 163, 206)-Net over F₂ — Digital

Digital (120, 163, 206)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−43, 163, 1791)-Net in Base 2 — Upper bound on s

There is no (120, 163, 1792)-net in base 2, because

1 times m-reduction [i] would yield (120, 162, 1792)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 847696 182530 618741 187915 708567 153612 025085 158001 > 2¹⁶² [i]