Abstract
In [Blokhuis and Lavrauw ( Geom. Dedicata 81 (2000), 231–243)] a construction of a class of two-intersection sets with respect to hyperplanes in PG( r−1, q t ), rt even, is given, with the same parameters as the union of ( q t/2 −1)/( q−1) disjoint Baer subgeometries if t is even and the union of ( q t −1)/( q−1) elements of an ( r/2−1)-spread in PG( r−1, q t ) 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.
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