MinT - Best Known (224−66, 224, s)-Nets in Base 2

Best Known (224−66, 224, s)-Nets in Base 2

(224−66, 224, 112)-Net over F₂ — Constructive and digital

Digital (158, 224, 112)-net over F₂, using

26 times m-reduction [i] based on digital (158, 250, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 125, 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]

(224−66, 224, 205)-Net over F₂ — Digital

Digital (158, 224, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−66, 224, 1406)-Net in Base 2 — Upper bound on s

There is no (158, 224, 1407)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 436940 157452 069552 610931 915771 999622 033940 674226 710364 335423 892960 > 2²²⁴ [i]