Hall and Jarrett [3] listed efficient generalized cyclic
designs, in a sense of maximizing the overall average efficiency factors,
with the parameters $10 \leq v \leq 60$ and $r<k \leq 10$. We consider a
method for constructing a generalized cyclic design with larger values of
the parameters from a generalized cyclic design and we give a relationship
between the efficiency factors of these designs. We present efficient
larger generalized cyclic designs with $v \leq 100$ and $r<k \leq 25$,
applying the method to the efficient cyclic designs listed by John [9], the
efficient generalized cyclic designs listed by Hall and Jarrett [3] and the
dual designs of these efficient designs. Most of the resulting generalized
cyclic designs have fairly high efficiency factors, it therefore seems that
the method is useful to construct efficient larger generalized cyclic
designs, provided that the original designs of this method are efficient.