Lifting of divisible designs

The aim of this paper is to present a construction of t-divisible designs for t > 3, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties are employed. More precisely, in a first step an abstract construction, called t-lifting, is developed. It starts from a set X containing a tdivisible design and a group G acting on X . Then several explicit examples are given, where X is a subset of PG(n, q) and G is a subgroup of GLn+1(q). In some cases X is obtained from a cone with a Veronesean or an h-sphere as its basis. In other examples X arises from a projective embedding of a Witt design. As a result, for any integer t ≥ 2 infinitely many non-isomorphic t-divisible designs are found. 2000 Mathematics Subject Classification. 05B30, 51E20, 20B25.