MinT - Best Known (134−31, 134, s)-Nets in Base 2

Best Known (134−31, 134, s)-Nets in Base 2

(134−31, 134, 144)-Net over F₂ — Constructive and digital

Digital (103, 134, 144)-net over F₂, using

4 times m-reduction [i] based on digital (103, 138, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 46, 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]

(134−31, 134, 248)-Net over F₂ — Digital

Digital (103, 134, 248)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−31, 134, 2976)-Net in Base 2 — Upper bound on s

There is no (103, 134, 2977)-net in base 2, because

1 times m-reduction [i] would yield (103, 133, 2977)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10914 130937 285704 913508 197120 277300 098048 > 2¹³³ [i]