MinT - Best Known (176−65, 176, s)-Nets in Base 2

Best Known (176−65, 176, s)-Nets in Base 2

(176−65, 176, 68)-Net over F₂ — Constructive and digital

Digital (111, 176, 68)-net over F₂, using

4 times m-reduction [i] based on digital (111, 180, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 90, 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]

(176−65, 176, 99)-Net over F₂ — Digital

Digital (111, 176, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−65, 176, 520)-Net in Base 2 — Upper bound on s

There is no (111, 176, 521)-net in base 2, because

1 times m-reduction [i] would yield (111, 175, 521)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 48820 516041 680570 737114 513923 260055 337775 531595 225648 > 2¹⁷⁵ [i]