MinT - Best Known (174−47, 174, s)-Nets in Base 2

Best Known (174−47, 174, s)-Nets in Base 2

(174−47, 174, 144)-Net over F₂ — Constructive and digital

Digital (127, 174, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 58, 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]

(174−47, 174, 205)-Net over F₂ — Digital

Digital (127, 174, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−47, 174, 1699)-Net in Base 2 — Upper bound on s

There is no (127, 174, 1700)-net in base 2, because

1 times m-reduction [i] would yield (127, 173, 1700)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12131 099486 449300 989253 168878 755450 246507 956515 618536 > 2¹⁷³ [i]