MinT - Best Known (225−98, 225, s)-Nets in Base 2

Best Known (225−98, 225, s)-Nets in Base 2

(225−98, 225, 66)-Net over F₂ — Constructive and digital

Digital (127, 225, 66)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 88, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (39, 137, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(225−98, 225, 84)-Net over F₂ — Digital

Digital (127, 225, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−98, 225, 392)-Net in Base 2 — Upper bound on s

There is no (127, 225, 393)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55 373015 251326 860071 417653 386729 851041 441890 446874 422882 773616 413456 > 2²²⁵ [i]