MinT - Best Known (173−49, 173, s)-Nets in Base 2

Best Known (173−49, 173, s)-Nets in Base 2

(173−49, 173, 112)-Net over F₂ — Constructive and digital

Digital (124, 173, 112)-net over F₂, using

9 times m-reduction [i] based on digital (124, 182, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 91, 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]

(173−49, 173, 181)-Net over F₂ — Digital

Digital (124, 173, 181)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−49, 173, 1373)-Net in Base 2 — Upper bound on s

There is no (124, 173, 1374)-net in base 2, because

1 times m-reduction [i] would yield (124, 172, 1374)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6051 699594 179786 937449 083812 213038 352450 822815 330927 > 2¹⁷² [i]