MinT - Best Known (177, 177+82, s)-Nets in Base 2

Best Known (177, 177+82, s)-Nets in Base 2

(177, 177+82, 112)-Net over F₂ — Constructive and digital

Digital (177, 259, 112)-net over F₂, using

t-expansion [i] based on digital (163, 259, 112)-net over F₂, using
- 1 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]

(177, 177+82, 196)-Net over F₂ — Digital

Digital (177, 259, 196)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+82, 1227)-Net in Base 2 — Upper bound on s

There is no (177, 259, 1228)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 950815 074925 713039 966360 113362 886579 255089 055365 358072 068606 375526 260466 264442 > 2²⁵⁹ [i]