Statistica Sinica 11(2001), 241-260

ON THE CONSTRUCTION OF

ASYMMETRIC ORTHOGONAL ARRAYS

Chung-yi Suen, Ashish Das$^*$ and Aloke Dey$^*$

Cleveland State University and $^*$Indian Statistical Institute

Abstract: A general method for constructing asymmetric orthogonal arrays of arbitrary strength is proposed. Application of this method is made to obtain several new families of tight asymmetric orthogonal arrays of strength three. A procedure for replacing a column with $2^{\nu }$ symbols in an orthogonal array of strength three by several 2-symbol columns, without disturbing the orthogonality of the array, leads to some new tight asymmetric orthogonal arrays of strength three. Some new families of asymmetric orthogonal arrays of strength four are also reported, and it is shown that these arrays accommodate the maximum number of columns for given values of other parameters of the array.

Key words and phrases: Arrays of strength three and four, Galois field, replacement procedure, tight arrays.