MinT - Best Known (225−61, 225, s)-Nets in Base 2

Best Known (225−61, 225, s)-Nets in Base 2

(225−61, 225, 195)-Net over F₂ — Constructive and digital

Digital (164, 225, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 75, 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]

(225−61, 225, 251)-Net over F₂ — Digital

Digital (164, 225, 251)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−61, 225, 2086)-Net in Base 2 — Upper bound on s

There is no (164, 225, 2087)-net in base 2, because

1 times m-reduction [i] would yield (164, 224, 2087)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 184982 287916 556060 980114 047020 370999 016372 316536 789926 871056 632820 > 2²²⁴ [i]