MinT - Best Known (186−70, 186, s)-Nets in Base 2

Best Known (186−70, 186, s)-Nets in Base 2

(186−70, 186, 68)-Net over F₂ — Constructive and digital

Digital (116, 186, 68)-net over F₂, using

4 times m-reduction [i] based on digital (116, 190, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 95, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(186−70, 186, 100)-Net over F₂ — Digital

Digital (116, 186, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−70, 186, 503)-Net in Base 2 — Upper bound on s

There is no (116, 186, 504)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 101 208938 235604 679203 271388 581241 418040 494408 350179 891633 > 2¹⁸⁶ [i]