MinT - Best Known (35, 47, s)-Nets in Base 2

Best Known (35, 47, s)-Nets in Base 2

(35, 47, 72)-Net over F₂ — Constructive and digital

Digital (35, 47, 72)-net over F₂, using

1 times m-reduction [i] based on digital (35, 48, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 16, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(35, 47, 99)-Net over F₂ — Digital

Digital (35, 47, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(35, 47, 674)-Net in Base 2 — Upper bound on s

There is no (35, 47, 675)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 141 554638 220536 > 2⁴⁷ [i]