MinT - Best Known (43, 43+17, s)-Nets in Base 2

Best Known (43, 43+17, s)-Nets in Base 2

(43, 43+17, 72)-Net over F₂ — Constructive and digital

Digital (43, 60, 72)-net over F₂, using

trace code for nets [i] based on digital (3, 20, 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]

(43, 43+17, 83)-Net over F₂ — Digital

Digital (43, 60, 83)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+17, 613)-Net in Base 2 — Upper bound on s

There is no (43, 60, 614)-net in base 2, because

1 times m-reduction [i] would yield (43, 59, 614)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 580472 939508 034652 > 2⁵⁹ [i]