  The geproci property is a recent development in the world of geometry. We
call a set of points $Z\subseteq\mathbb{P}_k^3$ an $(a,b)$-geproci set (for
GEneral PROjection is a Complete Intersection) if its projection from a general
point $P$ to a plane is a complete intersection of curves of degrees $a\leq b$.
Nondegenerate examples known as grids have been known since 2011. Nondegenerate
nongrids were found starting in 2018, working in characteristic 0. Almost all
of these new examples are of a special kind called half grids.
  Before the work in this paper -- based partly on the author's thesis -- only
a few examples of geproci nontrivial non-grid non-half grids were known and
there was no known way to generate more. Here, we use geometry in the positive
characteristic setting to give new methods of producing geproci half grids and
non-half grids.
