Upper bound on the number of multi-level columns in equally replicated optimal designs minimizing the E(fNOD) criterion

This article provides an upper bound on the number of multi-level columns, denoted by M, in equally replicated optimal designs, minimizing the E(fNOD) criterion. These designs are called E(fNOD)-optimal. Applying an algorithm and by row juxtaposition, fourteen E(fNOD)-optimal designs are constructed.