Ideals with larger projective dimension and regularity

► 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 by Caviglia (2004) and McCullough (2011). ► In particular, we describe a family of three-generated homogeneous ideals, in arbitrary characteristic, whose projective dimension grows asymptotically as a power of the degree of the generators.