On computer generation of balanced arrays

This paper provides an algebraic (and hence computing) procedure for generation of balanced arrays having two symbols, m rows, specified minimum and maximum column weights, arbitrary strength t≦m, and index set parameters μ^t₁, μ^t₂,…, μ^t_t. μ^t₀ is unspecified, and calculated as part of the algorithm, although the procedure for specifying it is straightforward and can be used if desired. Array generation is herein reduced to finding integral solutions to a linear programming problem. It is shown that the integral solutions of the system of equations comprise all balanced arrays with the given set of parameters.A computing algorithm is provided which constructs the system of equations to be solved; it has been interfaced with a standard linear programming package to provide some preliminary results.Additional algorithms whose development should result in substantial decreases in computing costs are discussed.