MinT - Best Known (31, 51, s)-Nets in Base 2

Best Known (31, 51, s)-Nets in Base 2

(31, 51, 34)-Net over F₂ — Constructive and digital

Digital (31, 51, 34)-net over F₂, using

1 times m-reduction [i] based on digital (31, 52, 34)-net over F₂, using
- trace code for nets [i] based on digital (5, 26, 17)-net over F₄, using
  - net from sequence [i] based on digital (5, 16)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
      - an explicitly constructive algebraic function field [i]

(31, 51, 35)-Net over F₂ — Digital

Digital (31, 51, 35)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(31, 51, 141)-Net in Base 2 — Upper bound on s

There is no (31, 51, 142)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2340 783043 227334 > 2⁵¹ [i]