Some Constructions of General Covering Designs

  • Federico Montecalvo
Keywords: covering design, Turán system, lotto design, block design


Given five positive integers $v, m,k,\lambda$ and $t$ where $v\geq k \geq t$ and $v \geq m \geq t,$ a $t$-$(v,k,m,\lambda)$ general covering design is a pair $(X,\mathcal{B})$ where $X$ is a set of $v$ elements (called points) and $\mathcal{B}$ a multiset of $k$-subsets of $X$ (called blocks) such that every $m$-subset of $X$ intersects (is covered by) at least $\lambda$ members of $\mathcal{B}$ in at least $t$ points. In this article we present new constructions for general covering designs and we generalize some others. By means of these constructions we will be able to obtain some new upper bounds on the minimum size of such designs.

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