MinT - Best Known (168, 168+72, s)-Nets in Base 2

Best Known (168, 168+72, s)-Nets in Base 2

(168, 168+72, 112)-Net over F₂ — Constructive and digital

Digital (168, 240, 112)-net over F₂, using

t-expansion [i] based on digital (163, 240, 112)-net over F₂, using
- 20 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+72, 208)-Net over F₂ — Digital

Digital (168, 240, 208)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+72, 1398)-Net in Base 2 — Upper bound on s

There is no (168, 240, 1399)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 803477 743142 579656 062584 811674 739355 900148 187397 523096 016097 259105 187355 > 2²⁴⁰ [i]