MinT - Best Known (133−55, 133, s)-Nets in Base 2

Best Known (133−55, 133, s)-Nets in Base 2

(133−55, 133, 54)-Net over F₂ — Constructive and digital

Digital (78, 133, 54)-net over F₂, using

3 times m-reduction [i] based on digital (78, 136, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 68, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(133−55, 133, 61)-Net over F₂ — Digital

Digital (78, 133, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−55, 133, 285)-Net in Base 2 — Upper bound on s

There is no (78, 133, 286)-net in base 2, because

1 times m-reduction [i] would yield (78, 132, 286)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5542 254660 555310 052729 085351 097403 558742 > 2¹³² [i]