Large sets of t -designs over finite fields

Nontrivial t-designs over finite fields exist for all t

A t-(n, k, λ) design over Fq is a collection of k-dimensional subspaces of Fq , called blocks, such that each t-dimensional subspace of Fq is contained in exactly λ blocks. Such t-designs over Fq are the q-analogs of conventional combinatorial designs. Nontrivial t-(n, k, λ) designs over Fq are currently known to exist only for t 6 3. Herein, we prove that simple (meaning, without repeated bloc...

Tactical decompositions of designs over finite fields

Abstract. An automorphism group of an incidence structure I induces a tactical decomposition on I. It is well known that tactical decompositions of t-designs satisfy certain necessary conditions which can be expressed as equations in terms of the coefficients of tactical decomposition matrices. In this article we present results obtained for tactical decompositions of q-analogs of t-designs, mo...

New t-designs and large sets of t-designs

Large sets of disjoint t-designs

[u this paper, we show how the basis reduction algorithm of Kreher and Radziszowski can be used to construct large sets of disjoint designs with specified automorphisms. In particular, we construct a (3,4,23;4)large set which rise to an infinite family of large sets of 4-desiglls via a result of Teirlinck [6].

Some small large sets of t-designs