A Technique for n2k Factorial Designs

Abstract

This article developed an appealing technique for n2k factorial designs that would generate more compact and more efficient computational results on n2k complete experiments that would be of immense benefit to students and researchers. The article leveraged on existing body of knowledge on 2k factorial designs to contrive and exploit a series of orthogonal and block diagonal matrices, which formed the basis for the statements and proofs of envisaged results on complete n2k experiments. The research effort culminated into statements and proofs of what the researcher referred to as Ukwu’s theorem and its corollary. These would elucidate the design process, offer computational advantages on the prosecution of complete n2k experiments, as well as enhance their mathematical appreciation. The utility and applicability of the results of the investigation should be multi-disciplinary in nature and scope.