On Two-Intersection Sets with Respect to Hyperplanes in Projective Spaces

In [Blokhuis and Lavrauw (Geom. Dedicata81 (2000), 231–243)] a construction of a class of two-intersection sets with respect to hyperplanes in PG(r−1,qt), rt even, is given, with the same parameters as the union of (qt/2−1)/(q−1) disjoint Baer subgeometries if t is even and the union of (qt−1)/(q−1) elements of an (r/2−1)-spread in PG(r−1,qt) if t is odd. In this paper, we prove that although they have the same parameters, they are different. This was previously proved in [Ball et al. (Finite Fields Appl.6 (2000), 294–301)] in the special case where r=3 and t=4.