In association rule mining, when the attributes have numerical values the usual method employed in deterministic approaches is to discretize them defining proper intervals. But the type and parameters of the discretization can affect notably the quality of the rules generated. This work presents a method based on a deterministic exploration of the interval search space, with no use of a previous discretization but the dynamic generation of intervals. The algorithm also employs auxiliary data structures and certain optimizations to reduce the search and improve the quality of the rules extracted. Some experiments have been performed comparing it with the well known deterministic Apriori algorithm. Also, the algorithm has been used for the extraction of association rules from a dataset with information about Sub-Saharan African countries, obtaining a variety of good-quality rules.