MinT - Best Known (224−76, 224, s)-Nets in Base 2

Best Known (224−76, 224, s)-Nets in Base 2

(224−76, 224, 112)-Net over F₂ — Constructive and digital

Digital (148, 224, 112)-net over F₂, using

6 times m-reduction [i] based on digital (148, 230, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 115, 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]

(224−76, 224, 148)-Net over F₂ — Digital

Digital (148, 224, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−76, 224, 838)-Net in Base 2 — Upper bound on s

There is no (148, 224, 839)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26 966080 322988 664651 433499 841336 369808 604742 103117 434599 502318 044390 > 2²²⁴ [i]