  Olmez, in "Symmetric $1\frac{1}{2}$-Designs and $1\frac{1}{2}$-Difference
Sets" (2014), introduced the concept of a partial geometric difference set
(also referred to as a $1\frac{1}{2}$-design), and showed that partial
geometric difference sets give partial geometric designs. Nowak et al., in
"Partial Geometric Difference Families" (2014), introduced the concept of a
partial difference family, and showed that these also give partial geometric
designs. It was shown by Brouwer et al. in "Directed strongly regular graphs
from $1\frac{1}{2}$-designs" (2012) that directed strongly regular graphs can
be obtained from partial geometric designs. In this correspondence we construct
several families of partial geometric difference sets and partial difference
families with new parameters, thereby giving directed strongly regular graphs
with new parameters. We also discuss some of the links between partially
balanced designs, $2$-adesigns (which were recently coined by Cunsheng Ding in
"Codes from Difference Sets" (2015)), and partial geometric designs, and make
an investigation into when a $2$-adesign is partial geometric.
