Finding New Fractions of Factorial Experimental Designs

A method of obtaining symmetrical balanced fractions of 3 n and 2 m 3 n factorial designs is proposed, based on an analysis of such designs into a complex of concentric hyperspheres in an n-dimensional factor space. Two examples are constructed, a half-replicate of a 34 design and a half-replicate of a 23 32 design. Analysis shows both designs to have useful properties and to be relatively easy to analyse. Comparison is made with a half-replicate of a 23 32 design recently published by W. S. Connor.