MinT - Best Known (72, 101, s)-Nets in Base 2

Best Known (72, 101, s)-Nets in Base 2

(72, 101, 75)-Net over F₂ — Constructive and digital

Digital (72, 101, 75)-net over F₂, using

1 times m-reduction [i] based on digital (72, 102, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 34, 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]

(72, 101, 116)-Net over F₂ — Digital

Digital (72, 101, 116)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 101, 834)-Net in Base 2 — Upper bound on s

There is no (72, 101, 835)-net in base 2, because

1 times m-reduction [i] would yield (72, 100, 835)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 285619 729264 244139 833312 103408 > 2¹⁰⁰ [i]