MinT - Best Known (214−69, 214, s)-Nets in Base 2

Best Known (214−69, 214, s)-Nets in Base 2

(214−69, 214, 112)-Net over F₂ — Constructive and digital

Digital (145, 214, 112)-net over F₂, using

10 times m-reduction [i] based on digital (145, 224, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 112, 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]

(214−69, 214, 160)-Net over F₂ — Digital

Digital (145, 214, 160)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−69, 214, 991)-Net in Base 2 — Upper bound on s

There is no (145, 214, 992)-net in base 2, because

1 times m-reduction [i] would yield (145, 213, 992)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13456 924262 905912 262577 715137 218954 199404 968396 149149 779616 980230 > 2²¹³ [i]