MinT - Best Known (168, 168+78, s)-Nets in Base 2

Best Known (168, 168+78, s)-Nets in Base 2

(168, 168+78, 112)-Net over F₂ — Constructive and digital

Digital (168, 246, 112)-net over F₂, using

t-expansion [i] based on digital (163, 246, 112)-net over F₂, using
- 14 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
  - trace code for nets [i] based on digital (33, 130, 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]

(168, 168+78, 187)-Net over F₂ — Digital

Digital (168, 246, 187)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+78, 1162)-Net in Base 2 — Upper bound on s

There is no (168, 246, 1163)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 113 561355 851744 364819 825883 174770 049503 617734 149458 149108 093221 960723 687216 > 2²⁴⁶ [i]