Unitals and replaceable t-nests

Abstract

Let Ū be a known unital of PG(2, q2), q odd, and let N be a t-nest in a regular spread S. Suppose we replace N by a replacement set N to form the new spread S' = (S\Ň) UŇ). Using the Bruck-Bose correspondence, we look at the afhne points of Ū in V{S) = PG(2,q 2) and see whether the corresponding afhne point set in the new plane V{S') can be completed to a unital.