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.
CAGGEGI A, FALCONE G (2007). On 2-(n^2,2n,2n-1) designs with three intersection numbers. DESIGNS, CODES AND CRYPTOGRAPHY, 43(1), 33-40 [10.1007/s10623-007-9051-z].
On 2-(n^2,2n,2n-1) designs with three intersection numbers
CAGGEGI, Andrea;FALCONE, Giovanni
2007-01-01
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.
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