MinT - Best Known (156, 156+56, s)-Nets in Base 2

Best Known (156, 156+56, s)-Nets in Base 2

(156, 156+56, 195)-Net over F₂ — Constructive and digital

Digital (156, 212, 195)-net over F₂, using

1 times m-reduction [i] based on digital (156, 213, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 71, 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]

(156, 156+56, 255)-Net over F₂ — Digital

Digital (156, 212, 255)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+56, 2107)-Net in Base 2 — Upper bound on s

There is no (156, 212, 2108)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6595 614814 102855 071816 553722 725303 396105 802278 874766 189295 988648 > 2²¹² [i]