Hedayat A.S., Sloane N.J.A., Stufken J. Orthogonal Arrays: Theory and Applications

Springer, 1999 – 416 p. - Who should read this book'? Anyone who is running experiments, whether in a chemistry lab or a manufacturing plant (trying to make those alloys stronger), or in agricultural or medical research. Any one interested in one of the most fascinating areas of discrete mathematics, connected to statistics and coding theory, with applications to computer science and cryptography. This is the first book on the subject since its introduction more than fifty years ago, and can be used as a graduate text or as a reference work. It features all of the key results, many very useful tables, and a large number of exercises and research problems. Most of the arrays that can be obtained by the methods in this book are available electronically. Orthogonal arrays are beautiful and useful. They are essential in statistics and they are used in computer science and cryptography. In statistics they are primarily used in designing experiments, which simply means that they are immensely important in all areas of human investigation: for example in medicine, agriculture and manufacturing. Your automobile lasts longer today because of orthogonal arrays. The mathematical theory is extremely beautiful: orthogonal arrays are related to combinatorics, finite fields, geometry and error-correcting codes. The definition of an orthogonal array is simple and natural, and we know many elegant constructions- yet there are at least as many unsolved problems.