Contractive lower triangular block Toeplitz (LTBT) matrices have recently been parametrized in a closed-form by a sequence of unstructured contractive matrices. A problem naturally arises between uniform samplings over contractive LTBT matrices and their matrix parameters, that is, which one is more appropriate in control system analysis and synthesis. This paper makes it clear that uniform sampling over matrix parameters results in a contractive LTBT matrix with a more rapid concentration speed towards the boundary of the uncertainty set. This is not an attractive property in control-related problems. Numerical comparisons also show that uniform sampling directly over contractive LTBT matrices outperforms that over the matrix parameter set in robustness analysis for a closed-loop system, as well as in strongly stable closed-loop system design with complexity constraints on the controller. As a sacrifice, uniform sampling over contractive LTBT matrices is more mathematically complicated and more time consuming.