### Some Constructions of General Covering Designs

#### Abstract

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.

#### Keywords

covering design; Turán system; lotto design; block design