MinT - Best Known (225−66, 225, s)-Nets in Base 2

Best Known (225−66, 225, s)-Nets in Base 2

(225−66, 225, 135)-Net over F₂ — Constructive and digital

Digital (159, 225, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 75, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(225−66, 225, 208)-Net over F₂ — Digital

Digital (159, 225, 208)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−66, 225, 1437)-Net in Base 2 — Upper bound on s

There is no (159, 225, 1438)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55 026386 645007 458053 832641 835612 041315 919533 223826 486656 927447 827828 > 2²²⁵ [i]