MinT - Best Known (170, 250, s)-Nets in Base 2

Best Known (170, 250, s)-Nets in Base 2

(170, 250, 112)-Net over F₂ — Constructive and digital

Digital (170, 250, 112)-net over F₂, using

t-expansion [i] based on digital (163, 250, 112)-net over F₂, using
- 10 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]

(170, 250, 186)-Net over F₂ — Digital

Digital (170, 250, 186)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 250, 1141)-Net in Base 2 — Upper bound on s

There is no (170, 250, 1142)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1812 451079 885235 237555 416336 250880 357046 811646 811914 443439 343818 620681 145746 > 2²⁵⁰ [i]