The paper addresses design of experiments for classifying the input factors
of a multi-variate function into negligible, linear and other
(non-linear/interaction) factors. We give constructive procedures for
completing the definition of the clustered designs proposed Morris 1991, that
become defined for arbitrary number of input factors and desired clusters'
multiplicity. Our work is based on a representation of subgraphs of the
hyper-cube by polynomials that allows the formal verification of the designs'
properties. Ability to generate these designs in a systematic manner opens new
perspectives for the characterisation of the behaviour of the function's
derivatives over the input space that may offer increased discrimination
