Hamming distances of tight orthogonal arrays

Abstract

Orthogonal arrays (OAs) are widely applied in the statistical design of experiments. The Hamming distances of OAs play an increasingly important role in various areas; however, it is difficult to use Hamming distances, especially for tight and mixed orthogonal arrays (MOAs). For example, two OAs with the same parameters may have distinct Hamming distances due to their different structures and constructions. In addition, studies on Hamming distances of tight OAs are scant, with the exception of a study indicating that a tight symmetrical OA of strength 2 has a constant Hamming distance. In this article, we calculate Hamming distances for high-strength OAs, including all tight symmetrical OAs of strength 3, 4, and 5. Interestingly, the Hamming distances do not depend on the constructions or structures of the arrays. Additionally, we study the Hamming distances of several classes of MOAs of strength 2 and 3, some of which are not related to the structures of the arrays.