Upper Bounds on the Maximal Number of Facets of 0/1-Polytopes

We prove two new upper bounds on the number of facets that a d -dimensional 0/1-polytope can have. The first one is 2(d − 1)! + 2(d − 1) (which is the best one currently known for small dimensions), while the second one of O((d − 2)!) is the best known bound for large dimensions.