MinT - Best Known (224−74, 224, s)-Nets in Base 2

Best Known (224−74, 224, s)-Nets in Base 2

(224−74, 224, 112)-Net over F₂ — Constructive and digital

Digital (150, 224, 112)-net over F₂, using

10 times m-reduction [i] based on digital (150, 234, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 117, 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]

(224−74, 224, 157)-Net over F₂ — Digital

Digital (150, 224, 157)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−74, 224, 919)-Net in Base 2 — Upper bound on s

There is no (150, 224, 920)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 019187 418490 324389 608183 263054 630121 890070 735179 177810 877618 706612 > 2²²⁴ [i]