MinT - Best Known (68, 95, s)-Nets in Base 2

Best Known (68, 95, s)-Nets in Base 2

(68, 95, 75)-Net over F₂ — Constructive and digital

Digital (68, 95, 75)-net over F₂, using

1 times m-reduction [i] based on digital (68, 96, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 32, 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]

(68, 95, 114)-Net over F₂ — Digital

Digital (68, 95, 114)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 95, 832)-Net in Base 2 — Upper bound on s

There is no (68, 95, 833)-net in base 2, because

1 times m-reduction [i] would yield (68, 94, 833)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19960 968046 793604 877032 052704 > 2⁹⁴ [i]