MinT - Best Known (71−23, 71, s)-Nets in Base 2

Best Known (71−23, 71, s)-Nets in Base 2

(71−23, 71, 56)-Net over F₂ — Constructive and digital

Digital (48, 71, 56)-net over F₂, using

1 times m-reduction [i] based on digital (48, 72, 56)-net over F₂, using
- trace code for nets [i] based on digital (12, 36, 28)-net over F₄, using
  - net from sequence [i] based on digital (12, 27)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(71−23, 71, 68)-Net over F₂ — Digital

Digital (48, 71, 68)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−23, 71, 388)-Net in Base 2 — Upper bound on s

There is no (48, 71, 389)-net in base 2, because

1 times m-reduction [i] would yield (48, 70, 389)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1195 544220 713085 676800 > 2⁷⁰ [i]