Summary: Testing equality of covariance matrices of \(k\) populations has long been an interesting issue in statistical inference. To overcome the sparseness of data points in a high-dimensional space and deal with the general cases, we suggest several projection pursuit type statistics. Some results on the limiting distributions of the statistics are obtained. Some properties of bootstrap approximations are investigated. Furthermore, for computational reasons an approximation which is based on the number theoretic method for the statistics is adopted. Several simulation experiments are performed.