MinT - Best Known (75, 75+39, s)-Nets in Base 2

Best Known (75, 75+39, s)-Nets in Base 2

(75, 75+39, 66)-Net over F₂ — Constructive and digital

Digital (75, 114, 66)-net over F₂, using

6 times m-reduction [i] based on digital (75, 120, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 60, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(75, 75+39, 84)-Net over F₂ — Digital

Digital (75, 114, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+39, 461)-Net in Base 2 — Upper bound on s

There is no (75, 114, 462)-net in base 2, because

1 times m-reduction [i] would yield (75, 113, 462)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10392 576065 969326 738216 604732 974984 > 2¹¹³ [i]