turkmath.org

Orthogonal arrays are used in the design of experiments in statistics, in computer science as well as in many fields of combinatorics. In this talk, I will give an application of orthogonal arrays to construct D-optimal discrete choice experiments. Later, I will address the existence problem of orthogonal arrays, and I will describe new algorithms to enumerate all orthogonal arrays with given parameters. Key techniques include eliminating significant space requirements, using previously-computed information on substructures in an efficient way. Computational results show these algorithms to be significantly faster than the prior state-of-the-art. Lastly, I will define the linear independence of Latin squares and I will state a basis for a linear space which contains all Latin squares. I will use this theory to study an asymptotic formula for the number of orthogonal arrays with three columns.