MinT - Best Known (116, 116+39, s)-Nets in Base 2

Best Known (116, 116+39, s)-Nets in Base 2

(116, 116+39, 144)-Net over F₂ — Constructive and digital

Digital (116, 155, 144)-net over F₂, using

t-expansion [i] based on digital (115, 155, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (115, 156, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 52, 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]

(116, 116+39, 224)-Net over F₂ — Digital

Digital (116, 155, 224)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+39, 2155)-Net in Base 2 — Upper bound on s

There is no (116, 155, 2156)-net in base 2, because

1 times m-reduction [i] would yield (116, 154, 2156)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22913 546616 670263 514736 345544 549251 055555 900690 > 2¹⁵⁴ [i]