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This report presents the results of research on the allocation of binary cartesian product database files across several stores (such as disks) which are accessible in parallel so that the average time required to perform the retrieval (by using several parallel accesses) of all buckets specified by a partial-match query is objective of constructing efficient packings of Hamming spheres in hypercubes. The viewpoint of binary cartesian product file allocation thus produced allowed in our research the creation of allocations for two particular sizes of the set of stores such that the average processing time for partial-match queries was smaller than that of the best allocation technique found in the literature for these same two cases. It also provides a framework in which good allocations for other particular sizes of the set of stores, and possibly for general sets of stores, might be found.