MinT - Best Known (152−53, 152, s)-Nets in Base 2

Best Known (152−53, 152, s)-Nets in Base 2

(152−53, 152, 68)-Net over F₂ — Constructive and digital

Digital (99, 152, 68)-net over F₂, using

4 times m-reduction [i] based on digital (99, 156, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 78, 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]

(152−53, 152, 100)-Net over F₂ — Digital

Digital (99, 152, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−53, 152, 553)-Net in Base 2 — Upper bound on s

There is no (99, 152, 554)-net in base 2, because

1 times m-reduction [i] would yield (99, 151, 554)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2905 392804 433153 581012 089438 691211 066965 861920 > 2¹⁵¹ [i]