Large sets of t-designs over finite fields

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Abstract

A t-(n,k,λ;q)-design is a set of k-dimensional subspaces, called blocks, of an n-dimensional vector space V over the finite field with q elements such that each t-dimensional subspace is contained in exactly λ blocks. A partition of the complete set of k-dimensional subspaces of V into disjoint t-(n,k,λ;q) designs is called a large set of t-designs over finite fields. In this paper we give the first nontrivial construction of such a large set with t2.

Keywords

q-Analogs
Designs over finite fields
Large sets
Automorphism group

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