Among the challenges that the COVID-19 pandemic outbreak revealed is the problem to reduce the number of tests required for identifying the virus carriers in order to contain the viral spread while preserving the tests reliability. To cope with this issue, a prevalence testing paradigm based on group testing and compressive sensing approach or GTCS was examined. In these settings, a non-adaptive group testing algorithm is designed to rule out sure-negative samples. Then, on the reduced problem, a compressive sensing algorithm is applied to decode the positives without requiring any further testing besides the initial test matrix designed for the group testing phase. The result is a single-round non-adaptive group testing - compressive sensing algorithm to identify the positive samples. In this paper, we propose a heuristic random method to construct the test design called $α-$random row design or $α-$RRD. In the $α-$RRD, a random test matrix is constructed such that each test aggregates at most $α$ samples in one group test or pool. The pooled tests are heuristically selected one by one such that samples that were previously selected in the same test are less likely to be aggregated together in a new test. We examined the performance of the $α-$RRD design within the GTCS paradigm for several values of $α$. The experiments were conducted on synthetic data. Our results show that, for some values of $α$, a reduction of up to 10 fold in the tests number can be achieved when $α-$RRD design is applied in the GTCS paradigm.