A survey on resolvable solutions of semi-regular and regular group divisible designs was presented by Saurabh et al. (Commun Stat-Theory Methods 52: 1946–1962, 2021). The resolvable designs are useful in information theory (Xu et al. in: International Workshop on High Mobility Wireless Communications (HMWC), 2015 and Kim et al. in IEEE Commun Lett, 11: 1970–1974, 2022), speeding up distributed computing (Konstantinidis and Ramamoorthy in IEEE/ACM Trans Network 28: 1657–1670, 2020) and mutually unbiased bases (Kumar and Maitra in Cryptogr Commun 14: 527–549, 2021). Here a survey on partially \(\alpha\) -resolvable solutions of regular group divisible designs under the range of \(r,k\le 10\) is presented. A \(\alpha\) -resolvable solution of block design \(D(v,b,r,k)\) requires the necessary condition: \(k\) divides \(v\alpha\) to hold for its existence but this condition is not necessary for partially \(\alpha\) -resolvable solution to exist and hence the range of parameters for \(v,k\) gets widened. The partially resolvable regular group divisible designs are also useful as key pre-distribution schemes (Lee and Stinson in: IEEE wireless communications and networking conference (WCN’ 05), IEEE communication society, 2005 and in J Comb Des 14: 251–269, 2006). Partially \(\alpha\) -resolvable solutions are obtained using generalized Conference matrices and circulant matrices. In the process we also obtain a class of nested group divisible designs.
