Custom-designed DNA arrays offer the possibility of simultaneously monitoring thousands of hybridization reactions. These arrays show great potential for many medical and scientific applications, such as polymorphism analysis and genotyping. Relatively high costs are associated with the need to specifically design and synthesize problem-specific arrays. Recently, an alternative approach was suggested that utilizes fixed, universal arrays. This approach presents an interesting design problem-the arrays should contain as many probes as possible, while minimizing experimental errors caused by cross-hybridization. We use a simple thermodynamic model to cast this design problem in a formal mathematical framework. Employing new combinatorial ideas, we derive an efficient construction for the design problem and prove that our construction is near-optimal.