Experimental Design Generated by Group Morphisms: An Introduction

When the key matrix fulfils a certain condition which ensures that the functions assigning treatments and blocks to experimental units are group morphisms, the DSIGN method (Patterson, 1976) can produce a wide variety of orthogonal asymmetrical fractional and block designs. A good method for analysing the properties of such designs is to introduce a canonical reparametrisation with parameters in the field ℂ of complex numbers (Bailey, 1982; Kobilinsky, 1985b, 1990). We give here a simplified presentation of the corresponding theory together with many practical examples.