MinT - Best Known (125−37, 125, s)-Nets in Base 2

Best Known (125−37, 125, s)-Nets in Base 2

(125−37, 125, 75)-Net over F₂ — Constructive and digital

Digital (88, 125, 75)-net over F₂, using

1 times m-reduction [i] based on digital (88, 126, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 42, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]

(125−37, 125, 126)-Net over F₂ — Digital

Digital (88, 125, 126)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−37, 125, 868)-Net in Base 2 — Upper bound on s

There is no (88, 125, 869)-net in base 2, because

1 times m-reduction [i] would yield (88, 124, 869)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21 270392 437422 287356 679376 221521 887124 > 2¹²⁴ [i]