MinT - Best Known (57, 57+27, s)-Nets in Base 2

Best Known (57, 57+27, s)-Nets in Base 2

(57, 57+27, 66)-Net over F₂ — Constructive and digital

Digital (57, 84, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 42, 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]

(57, 57+27, 77)-Net over F₂ — Digital

Digital (57, 84, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+27, 454)-Net in Base 2 — Upper bound on s

There is no (57, 84, 455)-net in base 2, because

1 times m-reduction [i] would yield (57, 83, 455)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9 701205 790445 340335 123424 > 2⁸³ [i]