MinT - Best Known (249−86, 249, s)-Nets in Base 2

Best Known (249−86, 249, s)-Nets in Base 2

(249−86, 249, 112)-Net over F₂ — Constructive and digital

Digital (163, 249, 112)-net over F₂, using

11 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 130, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(249−86, 249, 155)-Net over F₂ — Digital

Digital (163, 249, 155)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−86, 249, 872)-Net in Base 2 — Upper bound on s

There is no (163, 249, 873)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 922 696969 575025 665566 856444 189873 988944 516159 591503 652016 545798 436393 961048 > 2²⁴⁹ [i]