MinT - Best Known (129−53, 129, s)-Nets in Base 2

Best Known (129−53, 129, s)-Nets in Base 2

(129−53, 129, 54)-Net over F₂ — Constructive and digital

Digital (76, 129, 54)-net over F₂, using

3 times m-reduction [i] based on digital (76, 132, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 66, 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]

(129−53, 129, 61)-Net over F₂ — Digital

Digital (76, 129, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−53, 129, 283)-Net in Base 2 — Upper bound on s

There is no (76, 129, 284)-net in base 2, because

1 times m-reduction [i] would yield (76, 128, 284)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 352 065077 869461 798525 886556 954032 992155 > 2¹²⁸ [i]