MinT - Best Known (107, 107+39, s)-Nets in Base 2

Best Known (107, 107+39, s)-Nets in Base 2

(107, 107+39, 135)-Net over F₂ — Constructive and digital

Digital (107, 146, 135)-net over F₂, using

1 times m-reduction [i] based on digital (107, 147, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 49, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(107, 107+39, 183)-Net over F₂ — Digital

Digital (107, 146, 183)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+39, 1544)-Net in Base 2 — Upper bound on s

There is no (107, 146, 1545)-net in base 2, because

1 times m-reduction [i] would yield (107, 145, 1545)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 44 830380 327986 830928 756787 990020 233222 743808 > 2¹⁴⁵ [i]