MinT - Best Known (176−69, 176, s)-Nets in Base 2

Best Known (176−69, 176, s)-Nets in Base 2

(176−69, 176, 66)-Net over F₂ — Constructive and digital

Digital (107, 176, 66)-net over F₂, using

8 times m-reduction [i] based on digital (107, 184, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 92, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(176−69, 176, 87)-Net over F₂ — Digital

Digital (107, 176, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−69, 176, 431)-Net in Base 2 — Upper bound on s

There is no (107, 176, 432)-net in base 2, because

1 times m-reduction [i] would yield (107, 175, 432)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49925 035007 191984 408906 306374 223849 094684 985047 008241 > 2¹⁷⁵ [i]