ACKNOWLEDGEMENT

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grants A9373, 0011 and by the Fonds pour la Formation de Chercheurs et l'Aide á la Recherche under Grant EQ2369.

INTRODUCTION

A finite projective plane of order n is a collection of n2+n+1 lines and n2+n+1 points such that

1. (1.1) every line contains n+1 points,

2. (1.2) every point is on n+1 lines,

3. (1.3) any two distinct lines intersect at exactly one point, and

4. (1.4) any two distinct points lie on exactly one line.

For example, a projective plane of order 2 is shown in Fig. 1. It has 7 points and 7 lines. The points are numbered from 1 to 7. The 7 lines are L1 = {1,2,4}, L2= {2,3,5}, L3 = {3,4,6}, L4= {4,5,7}, L5 {1,5,6}, L6 {2,6,7} and L7 = {1,3,7}. In Fig. 1 all the lines except L6 are drawn as straight lines. One can easily show that this projective plane of order 2 is unique up to the relabelling of points and lines.

Another way to represent a projective plane is to use an incidence matrix A of size n2 +n+ 1 by n2+n+1.