When forming core subsets, accessions from a collection are classified into clusters, and then samples are drawn from the clusters with the aim of maintaining the diversity of the collection. Core subsets can also be formed by sampling accessions from the entire collection without any previous stratification. Formation of core subsets can be done using phenotypic or genotypic data and statistical method can be used to group accessions into homogeneous clusters. In a stratified sampling strategy, the allocation method provides a criterion for determining the number of accessions to be selected from each cluster. An allocation method named the D method has been proposed for determining the number of accession to be selected from each cluster. In the D method, the number of accessions selected from each cluster is proportional to the mean of the distance between accessions within the cluster. Results using phenotypic and genotypic data show that if the collection needs to be stratafied the D allocation method produced samples with significantly more diversity than the other allocation methods. If the original collection does need to be stratified, a systematic method for sampling accession from the collection produces core subsets with more diversity than other sampling strategies. Computational enumeration (exhaustive) methods and local search (heuristic) algorithms together with the D method gave valuable approaches for forming more diverse core subsets than other strategies. Several sampling strategies were compared with the M strategy implemented in the MSTRAT algorithm.