Constructions of unitals in Desarguesian planes

We present a new construction of non-classical unitals from a classical unital U in PG ( 2 , q 2 ) . The resulting non-classical unitals are B–M unitals. The idea is to find a non-standard model Π of PG ( 2 , q 2 ) with the following three properties: (i) of Π are those of PG ( 2 , q 2 ) ; of Π are certain lines and conics of PG ( 2 , q 2 ) ; ints in U form a non-classical B–M unital in Π . onstruction also works for the B–T unital, provided that conics are replaced by certain algebraic curves of higher degree.