MinT - Best Known (112, 112+31, s)-Nets in Base 2

Best Known (112, 112+31, s)-Nets in Base 2

(112, 112+31, 195)-Net over F₂ — Constructive and digital

Digital (112, 143, 195)-net over F₂, using

4 times m-reduction [i] based on digital (112, 147, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 49, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(112, 112+31, 314)-Net over F₂ — Digital

Digital (112, 143, 314)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+31, 4522)-Net in Base 2 — Upper bound on s

There is no (112, 143, 4523)-net in base 2, because

1 times m-reduction [i] would yield (112, 142, 4523)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 577501 818785 702623 508057 788342 556946 262096 > 2¹⁴² [i]