# recreational mathematics

## Combinatorial covering designs ★

Author(s): Gordon; Mills; Rödl; Schönheim

A *covering design*, or *covering*, is a family of -subsets, called *blocks*, chosen from a -set, such that each -subset is contained in at least one of the blocks. The number of blocks is the covering’s *size*, and the minimum size of such a covering is denoted by .

**Problem**Find a closed form, recurrence, or better bounds for . Find a procedure for constructing minimal coverings.

Keywords: recreational mathematics