MinT - Best Known (168−41, 168, s)-Nets in Base 2

Best Known (168−41, 168, s)-Nets in Base 2

(168−41, 168, 195)-Net over F₂ — Constructive and digital

Digital (127, 168, 195)-net over F₂, using

t-expansion [i] based on digital (126, 168, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 56, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(168−41, 168, 258)-Net over F₂ — Digital

Digital (127, 168, 258)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−41, 168, 2680)-Net in Base 2 — Upper bound on s

There is no (127, 168, 2681)-net in base 2, because

1 times m-reduction [i] would yield (127, 167, 2681)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 188 103819 383327 748954 067864 319211 858929 155251 156638 > 2¹⁶⁷ [i]