We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positive and negative temperatures follow the second-order high-temperature series expansions for |T| > 3 nK. Our findings do not agree with the measurements of the former Rh experiment in Helsinki, where a deviation is seen at much higher temperatures.