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Günter Rote:

#
An Upper Bound on the Number of Facets of a 0-1-Polytope

*Draft, December 1996, 3 pages*
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Abstract

A 0-1-polytope in d dimensions has at most 6.4*d!/sqrt(d) facets.
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Note

Volker
Kaibel has recently (August 1997) shown a better bound of 2*(d-1)!
by a very simple argument. Tamás
Fleiner has further improved the bound to O((d-2)!) (September 1997).
A list of
the best lower bounds for the number of facets is maintained by Ulrich
Kortenkamp.