Abstract

Combinatorial arrangements now known as orthogonal arrays were introduced for use in statistics in the 1940’s. The primary purpose for their introduction was to guide the selection of level combinations in a fractional factorial experiment, and this is still an important reason for their interest in statistics. Various criteria based on statistical properties have been introduced over the years to distinguish between different orthogonal arrays of the same size, and some authors have attempted to enumerate all non-isomorphic arrays of small sizes. Orthogonal arrays also possess interesting relationships to several other combinatorial arrangements, including to error-correcting codes and Hadamard matrices. In this talk, aimed at a general mathematical audience, we will present a brief and selective overview of orthogonal arrays, including their existence, construction, and relationships to other arrangements.