MinT - Best Known (191−73, 191, s)-Nets in Base 2

Best Known (191−73, 191, s)-Nets in Base 2

(191−73, 191, 68)-Net over F₂ — Constructive and digital

Digital (118, 191, 68)-net over F₂, using

3 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]

(191−73, 191, 99)-Net over F₂ — Digital

Digital (118, 191, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−73, 191, 502)-Net in Base 2 — Upper bound on s

There is no (118, 191, 503)-net in base 2, because

1 times m-reduction [i] would yield (118, 190, 503)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1596 075458 312553 430538 237780 127569 999280 801333 983983 171047 > 2¹⁹⁰ [i]