Characterizing Geometric Designs

Abstract

We conjecture that the classical geometric 2-designs PGd(n, q), where 2 ≤ d ≤ n − 1, are characterized among all designs with the same parameters as those having line size q + 1. The conjecture is known to hold for the case d = n − 1 (the Dembowski-Wagner theorem) and also for d = 2 (a recent result established by Tonchev and the present author). Here we extend this result to the cases d = 3 and d = 4. The general case remains open and seems to be difficult.

Keywords

• projective space
• block designs