MinT - Best Known (186−53, 186, s)-Nets in Base 2

Best Known (186−53, 186, s)-Nets in Base 2

(186−53, 186, 135)-Net over F₂ — Constructive and digital

Digital (133, 186, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 62, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(186−53, 186, 190)-Net over F₂ — Digital

Digital (133, 186, 190)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−53, 186, 1424)-Net in Base 2 — Upper bound on s

There is no (133, 186, 1425)-net in base 2, because

1 times m-reduction [i] would yield (133, 185, 1425)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 098695 638980 264943 095638 849355 363768 477988 319452 263808 > 2¹⁸⁵ [i]