Lattice square approach to construction of mutually orthogonalF-squares

Summary Factorial design theory has been effectively used in solving problems associated with many combinatorial structures. Hedayat, Raghavarao and Seiden [7] clearly demonstrated this in obtaining various results onF(n, λ)-squares. Indeed, both theorems in their paper are cute observations if knowledge of factorial design theory is assumed. The objective of this paper is to present the lattice square method for obtaining sets of mutually orthogonalF(n, λ)-squares of given ordern. As a by-product a generalization of a theorem, due to the above authors, is obtained and a lower bound is presented for the number of mutually orthogonalF(n, λ)-squares on sets of various cardinalities associated with the canonical decomposition ofn as a product of powers of distinct primes.