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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… (More)

In this paper both blocking sets with respect to the s-subspaces and covers with t-subspaces in a finite Grassmannian are investigated, especially focusing on geometric descriptions of blocking sets and covers of minimum size. When such a description exists, it is called a Bose–Burton type theorem. The canonical example of a blocking set with respect to the… (More)

Let χ be a linear morphism of the product of two projective spaces PG(n, F) and PG(m, F) into a projective space. Let γ be the Segre embedding of such a product. In this paper we give some sufficient conditions for the existence of an automorphism α of the product space and a linear morphism of projective spaces ϕ, such that γϕ = αχ. A.M.S. classification… (More)

The generalized chain geometry over the local ring K(ε; σ) of twisted dual numbers, where K is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as well as a geometric model in 4-space are investigated. 1 Preliminaries This paper deals with a special class of divisible designs,… (More)