MinT - Best Known (225−96, 225, s)-Nets in Base 2

Best Known (225−96, 225, s)-Nets in Base 2

(225−96, 225, 66)-Net over F₂ — Constructive and digital

Digital (129, 225, 66)-net over F₂, using

3 times m-reduction [i] based on digital (129, 228, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 114, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(225−96, 225, 88)-Net over F₂ — Digital

Digital (129, 225, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−96, 225, 415)-Net in Base 2 — Upper bound on s

There is no (129, 225, 416)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 54 491310 005489 864714 890141 376926 987599 585182 032893 179240 242902 821108 > 2²²⁵ [i]