MinT - Best Known (176, 176+74, s)-Nets in Base 2

Best Known (176, 176+74, s)-Nets in Base 2

(176, 176+74, 135)-Net over F₂ — Constructive and digital

Digital (176, 250, 135)-net over F₂, using

2¹ times duplication [i] based on digital (175, 249, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 83, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(176, 176+74, 223)-Net over F₂ — Digital

Digital (176, 250, 223)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+74, 1530)-Net in Base 2 — Upper bound on s

There is no (176, 250, 1531)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1835 617058 742624 031295 477604 266364 557034 769397 444964 397641 914325 782782 336256 > 2²⁵⁰ [i]