MinT - Best Known (134−37, 134, s)-Nets in Base 2

Best Known (134−37, 134, s)-Nets in Base 2

(134−37, 134, 102)-Net over F₂ — Constructive and digital

Digital (97, 134, 102)-net over F₂, using

1 times m-reduction [i] based on digital (97, 135, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 45, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(134−37, 134, 158)-Net over F₂ — Digital

Digital (97, 134, 158)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−37, 134, 1239)-Net in Base 2 — Upper bound on s

There is no (97, 134, 1240)-net in base 2, because

1 times m-reduction [i] would yield (97, 133, 1240)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10939 906094 675922 649876 782763 819865 724853 > 2¹³³ [i]