MinT - Best Known (80, 80+33, s)-Nets in Base 2

Best Known (80, 80+33, s)-Nets in Base 2

(80, 80+33, 75)-Net over F₂ — Constructive and digital

Digital (80, 113, 75)-net over F₂, using

1 times m-reduction [i] based on digital (80, 114, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 38, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]

(80, 80+33, 120)-Net over F₂ — Digital

Digital (80, 113, 120)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+33, 847)-Net in Base 2 — Upper bound on s

There is no (80, 113, 848)-net in base 2, because

1 times m-reduction [i] would yield (80, 112, 848)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5265 007982 224386 461854 206429 926484 > 2¹¹² [i]