MinT - Best Known (54, 54+24, s)-Nets in Base 2

Best Known (54, 54+24, s)-Nets in Base 2

(54, 54+24, 66)-Net over F₂ — Constructive and digital

Digital (54, 78, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 39, 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]

(54, 54+24, 82)-Net over F₂ — Digital

Digital (54, 78, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+24, 461)-Net in Base 2 — Upper bound on s

There is no (54, 78, 462)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 306236 587084 901032 218229 > 2⁷⁸ [i]