MinT - Best Known (56−17, 56, s)-Nets in Base 2

Best Known (56−17, 56, s)-Nets in Base 2

(56−17, 56, 54)-Net over F₂ — Constructive and digital

Digital (39, 56, 54)-net over F₂, using

2 times m-reduction [i] based on digital (39, 58, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 29, 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]

(56−17, 56, 67)-Net over F₂ — Digital

Digital (39, 56, 67)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−17, 56, 430)-Net in Base 2 — Upper bound on s

There is no (39, 56, 431)-net in base 2, because

1 times m-reduction [i] would yield (39, 55, 431)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 36371 247349 563119 > 2⁵⁵ [i]