On 2-(n^2,2n,2n-1) designs with three intersection numbers

Abstract

The simple incidence structure D(A,2), formed by the points and the unordered pairs of distinct parallel lines of a finite affine plane A = (P,L) of order n > 4, is a 2 - (n 2,2n,2n-1) design with intersection numbers 0,4,n. In this paper, we show that the converse is true, when n > 5 is an odd integer.