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 pr
ocedure for replacing a column with 2(V) symbols in an orthogonal array of
strength three by several 2-symbol columns, without disturbing the orthogon
ality of the array, leads to some new tight asymmetric orthogonal arrays of
strength three. Some new families of asymmetric orthogonal arrays of stren
gth four are also reported, and it is shown that these arrays accommodate t
he maximum number of columns for given values of other parameters of the ar
ray.