MinT - Best Known (250−90, 250, s)-Nets in Base 2

Best Known (250−90, 250, s)-Nets in Base 2

(250−90, 250, 112)-Net over F₂ — Constructive and digital

Digital (160, 250, 112)-net over F₂, using

4 times m-reduction [i] based on digital (160, 254, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 127, 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]

(250−90, 250, 142)-Net over F₂ — Digital

Digital (160, 250, 142)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−90, 250, 764)-Net in Base 2 — Upper bound on s

There is no (160, 250, 765)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1870 231146 640255 098987 109547 108147 030322 595328 185246 568691 321242 229420 073398 > 2²⁵⁰ [i]