MinT - Best Known (117, 117+41, s)-Nets in Base 2

Best Known (117, 117+41, s)-Nets in Base 2

(117, 117+41, 144)-Net over F₂ — Constructive and digital

Digital (117, 158, 144)-net over F₂, using

1 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+41, 210)-Net over F₂ — Digital

Digital (117, 158, 210)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+41, 1886)-Net in Base 2 — Upper bound on s

There is no (117, 158, 1887)-net in base 2, because

1 times m-reduction [i] would yield (117, 157, 1887)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 183282 955251 088041 740312 372793 979002 939024 552259 > 2¹⁵⁷ [i]