Optimal design: Some geometrical aspects of D-optimality

SUMMARY The duality relationships between D-type optimal designs and problems of covering a subset of Euclidean space by central ellipsoids and ellipsoidal cylinders are described and consequences that aid the solution of either problem are discussed. It is shown that there are also design duals for the problems of finding minimal covering spheres and ellipsoids or cylinders whose centres or axes are chosen optimally.