We define a family of homogeneous ideals with large projective dimension and
regularity relative to the number of generators and their common degree. This
family subsumes and improves upon constructions given in [Cav04] and [McC]. In
particular, we describe a family of three-generated homogeneous ideals in
arbitrary characteristic whose projective dimension grows asymptotically as
sqrt{d}^(sqrt(d) - 1).