MinT - Best Known (156, 156+57, s)-Nets in Base 2

Best Known (156, 156+57, s)-Nets in Base 2

(156, 156+57, 195)-Net over F₂ — Constructive and digital

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+57, 248)-Net over F₂ — Digital

Digital (156, 213, 248)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+57, 2107)-Net in Base 2 — Upper bound on s

There is no (156, 213, 2108)-net in base 2, because

1 times m-reduction [i] would yield (156, 212, 2108)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6595 614814 102855 071816 553722 725303 396105 802278 874766 189295 988648 > 2²¹² [i]