MinT - Best Known (107−31, 107, s)-Nets in Base 2

Best Known (107−31, 107, s)-Nets in Base 2

(107−31, 107, 75)-Net over F₂ — Constructive and digital

Digital (76, 107, 75)-net over F₂, using

1 times m-reduction [i] based on digital (76, 108, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 36, 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]

(107−31, 107, 118)-Net over F₂ — Digital

Digital (76, 107, 118)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−31, 107, 839)-Net in Base 2 — Upper bound on s

There is no (76, 107, 840)-net in base 2, because

1 times m-reduction [i] would yield (76, 106, 840)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 82 075349 148455 167223 666582 444408 > 2¹⁰⁶ [i]