  We give two "lifting" constructions of strongly regular Cayley graphs. In the
first construction we "lift" a cyclotomic strongly regular graph by using a
subdifference set of the Singer difference set. The second construction uses
quadratic forms over finite fields and it is a common generalization of the
construction of the affine polar graphs \cite{CK86} and a construction of
strongly regular Cayley graphs given in \cite{FWXY}. The two constructions are
related in the following way: The second construction can be viewed as a
recursive construction, and the strongly regular Cayley graphs obtained from
the first construction can serve as starters for the second construction. We
also obtain association schemes from the second construction.

Combinatorics