MinT - Best Known (128, 211, s)-Nets in Base 2

Best Known (128, 211, s)-Nets in Base 2

(128, 211, 68)-Net over F₂ — Constructive and digital

Digital (128, 211, 68)-net over F₂, using

3 times m-reduction [i] based on digital (128, 214, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 107, 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]

(128, 211, 100)-Net over F₂ — Digital

Digital (128, 211, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 211, 503)-Net in Base 2 — Upper bound on s

There is no (128, 211, 504)-net in base 2, because

1 times m-reduction [i] would yield (128, 210, 504)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1656 580535 729673 558168 212381 205345 366581 871080 215483 029077 483970 > 2²¹⁰ [i]