A combinatorial approach was recently proposed for designing multidimensional codebooks for fading channels. Albeit flexible and granting full signal space diversity, it relies on the optimal maximum likelihood detection, which is rather complex. In this work, we propose an alternative low-complexity, list-based detection algorithm for the codebooks under this approach. The detection complexity of the proposed algorithm is analyzed, and simulation results for both detection complexity and error performance are presented. It is concluded that the proposed detection algorithm not only preserves the diversity gain but also presents an excellent performance-complexity trade-off, thus adding value to the combinatorial approach.