MinT - Best Known (129−52, 129, s)-Nets in Base 2

Best Known (129−52, 129, s)-Nets in Base 2

(129−52, 129, 56)-Net over F₂ — Constructive and digital

Digital (77, 129, 56)-net over F₂, using

1 times m-reduction [i] based on digital (77, 130, 56)-net over F₂, using
- trace code for nets [i] based on digital (12, 65, 28)-net over F₄, using
  - net from sequence [i] based on digital (12, 27)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(129−52, 129, 63)-Net over F₂ — Digital

Digital (77, 129, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−52, 129, 292)-Net in Base 2 — Upper bound on s

There is no (77, 129, 293)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 726 217103 403916 645941 705153 514852 574392 > 2¹²⁹ [i]