Construction of some asymmetrical orthogonal arrays

A method of construction of asymmetrical orthogonal arrays of strength two is described. The method exploits difference matrices and a special type of orthogonal arrays. Several families of asymmetrical orthogonal arrays are obtained through the method. An open problem relating to the construction of a class of asymmetrical orthogonal arrays is proposed and comments on partial solutions to the problem are made. A conjecture on an upper bound to the number of constraints in a class of arrays is also made.