MinT - Best Known (186−59, 186, s)-Nets in Base 2

Best Known (186−59, 186, s)-Nets in Base 2

(186−59, 186, 112)-Net over F₂ — Constructive and digital

Digital (127, 186, 112)-net over F₂, using

2 times m-reduction [i] based on digital (127, 188, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 94, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(186−59, 186, 147)-Net over F₂ — Digital

Digital (127, 186, 147)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−59, 186, 929)-Net in Base 2 — Upper bound on s

There is no (127, 186, 930)-net in base 2, because

1 times m-reduction [i] would yield (127, 185, 930)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 858437 922223 065362 739639 346681 369031 875283 882625 616424 > 2¹⁸⁵ [i]