MinT - Best Known (117, 117+39, s)-Nets in Base 2

Best Known (117, 117+39, s)-Nets in Base 2

(117, 117+39, 144)-Net over F₂ — Constructive and digital

Digital (117, 156, 144)-net over F₂, using

3 times m-reduction [i] based on digital (117, 159, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 53, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(117, 117+39, 229)-Net over F₂ — Digital

Digital (117, 156, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+39, 2236)-Net in Base 2 — Upper bound on s

There is no (117, 156, 2237)-net in base 2, because

1 times m-reduction [i] would yield (117, 155, 2237)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 45775 290802 820120 499959 399988 991681 585562 056704 > 2¹⁵⁵ [i]