On the Construction of Cyclic Collineations for Obtaining a Balanced Set of $L$-Restrictional Prime-Powered Lattice Designs

Abstract

Raktoe [3] has recently developed a procedure for obtaining a balanced confounding scheme for any $l$-restrictional lattice design of $s^m$ treatments where $s$ is a prime or a power of a prime and $m$ is a positive integer. He has shown that the generators of the confounding scheme in each arrangement can be taken from the columns of different powers of the rational canonical form of a matrix of cyclic collineation of a particular order. However, he did not indicate how to construct the generator matrices analytically except for the case $s = p = 2$. In all other cases, he obtained these matrices empirically. The present paper gives an analytic method for constructing the generator matrices of collineations for all values of $s$, by the application of a particular theorem in projective geometry and another one from group theory.