MinT - Best Known (186−71, 186, s)-Nets in Base 2

Best Known (186−71, 186, s)-Nets in Base 2

(186−71, 186, 68)-Net over F₂ — Constructive and digital

Digital (115, 186, 68)-net over F₂, using

2 times m-reduction [i] based on digital (115, 188, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 94, 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]

(186−71, 186, 97)-Net over F₂ — Digital

Digital (115, 186, 97)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−71, 186, 492)-Net in Base 2 — Upper bound on s

There is no (115, 186, 493)-net in base 2, because

1 times m-reduction [i] would yield (115, 185, 493)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 50 021329 499743 811901 432479 953899 727137 044123 633068 169984 > 2¹⁸⁵ [i]