MinT - Best Known (187−79, 187, s)-Nets in Base 2

Best Known (187−79, 187, s)-Nets in Base 2

(187−79, 187, 60)-Net over F₂ — Constructive and digital

Digital (108, 187, 60)-net over F₂, using

3 times m-reduction [i] based on digital (108, 190, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 95, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(187−79, 187, 77)-Net over F₂ — Digital

Digital (108, 187, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−79, 187, 365)-Net in Base 2 — Upper bound on s

There is no (108, 187, 366)-net in base 2, because

1 times m-reduction [i] would yield (108, 186, 366)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105 014887 677788 677155 148180 852055 316481 444044 226852 051104 > 2¹⁸⁶ [i]