Statistica Sinica 15(2005), 731-749

ORTHOGONAL ARRAYS OF STRENGTH THREE AND

SIZE $\mbf {2^r}$

Chung-yi Suen

Cleveland State University

Abstract: The paper attempts to construct all orthogonal arrays of strength three and size $2^r$. Methods for constructing asymmetric orthogonal arrays are developed. By using the theories of finite field and finite projective geometry, several new series of orthogonal arrays are obtained. Many other orthogonal arrays are derived from the new series. A list of parameters of known symmetric and asymmetric orthogonal arrays of strength three and size $2^r$ ($r \le 8$) is provided. Parameters of unknown orthogonal arrays which satisfy Rao's bound are also included in the list.

Key words and phrases: Finite field, finite projective geometry, geometric, orthogonal array, oval, ovaloid, resolution IV plan, tight.