MinT - Best Known (101, 101+31, s)-Nets in Base 2

Best Known (101, 101+31, s)-Nets in Base 2

(101, 101+31, 144)-Net over F₂ — Constructive and digital

Digital (101, 132, 144)-net over F₂, using

3 times m-reduction [i] based on digital (101, 135, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 45, 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]

(101, 101+31, 235)-Net over F₂ — Digital

Digital (101, 132, 235)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+31, 2711)-Net in Base 2 — Upper bound on s

There is no (101, 132, 2712)-net in base 2, because

1 times m-reduction [i] would yield (101, 131, 2712)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2724 505844 641769 762699 599007 607479 203878 > 2¹³¹ [i]