DNA microarrays constitute an in vitro example system of a highly crowded molecular recognition environment. Although they are widely applied in many biological applications, some of the basic mechanisms of the hybridization processes of DNA remain poorly understood. On a microarray, cross-hybridization arises from similarities of sequences that may introduce errors during the transmission of information. Experimentally, we determine an appropriate distance, called minimum Hamming distance, in which the sequences of a set differ. By applying an algorithm based on a graph-theoretical method, we find large orthogonal sets of sequences that are sufficiently different not to exhibit any cross-hybridization. To create such a set, we first derive an analytical solution for the number of sequences that include at least four guanines in a row for a given sequence length and eliminate them from the list of candidate sequences. We experimentally confirm the orthogonality of the largest possible set with a size of 23 for the length of 7. We anticipate our work to be a starting point toward the study of signal propagation in highly competitive environments, besides its obvious application in DNA high throughput experiments.