MinT - Best Known (133−31, 133, s)-Nets in Base 2

Best Known (133−31, 133, s)-Nets in Base 2

(133−31, 133, 144)-Net over F₂ — Constructive and digital

Digital (102, 133, 144)-net over F₂, using

t-expansion [i] based on digital (101, 133, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (101, 135, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 45, 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]

(133−31, 133, 242)-Net over F₂ — Digital

Digital (102, 133, 242)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−31, 133, 2841)-Net in Base 2 — Upper bound on s

There is no (102, 133, 2842)-net in base 2, because

1 times m-reduction [i] would yield (102, 132, 2842)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5469 179078 006416 960074 014602 842163 606328 > 2¹³² [i]