MinT - Best Known (83, 83+37, s)-Nets in Base 2

Best Known (83, 83+37, s)-Nets in Base 2

(83, 83+37, 72)-Net over F₂ — Constructive and digital

Digital (83, 120, 72)-net over F₂, using

trace code for nets [i] based on digital (3, 40, 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]

(83, 83+37, 111)-Net over F₂ — Digital

Digital (83, 120, 111)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+37, 712)-Net in Base 2 — Upper bound on s

There is no (83, 120, 713)-net in base 2, because

1 times m-reduction [i] would yield (83, 119, 713)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 676187 738659 666512 306011 047018 481504 > 2¹¹⁹ [i]