MinT - Best Known (125, 125+43, s)-Nets in Base 2

Best Known (125, 125+43, s)-Nets in Base 2

(125, 125+43, 144)-Net over F₂ — Constructive and digital

Digital (125, 168, 144)-net over F₂, using

3 times m-reduction [i] based on digital (125, 171, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 57, 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]

(125, 125+43, 229)-Net over F₂ — Digital

Digital (125, 168, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+43, 2119)-Net in Base 2 — Upper bound on s

There is no (125, 168, 2120)-net in base 2, because

1 times m-reduction [i] would yield (125, 167, 2120)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 188 906878 134895 464173 353918 535668 277973 930049 695972 > 2¹⁶⁷ [i]