MinT - Best Known (189−71, 189, s)-Nets in Base 2

Best Known (189−71, 189, s)-Nets in Base 2

(189−71, 189, 68)-Net over F₂ — Constructive and digital

Digital (118, 189, 68)-net over F₂, using

5 times m-reduction [i] based on digital (118, 194, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 97, 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]

(189−71, 189, 101)-Net over F₂ — Digital

Digital (118, 189, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−71, 189, 525)-Net in Base 2 — Upper bound on s

There is no (118, 189, 526)-net in base 2, because

1 times m-reduction [i] would yield (118, 188, 526)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 397 500179 828611 708834 476549 582351 304869 417683 185521 057312 > 2¹⁸⁸ [i]