  A graph is $n$-e.c. ($n$-existentially closed) if for every pair of subsets
  $A, B$ of vertex set $V$ of the graph such that $A \cap B = \emptyset$ and
  $|A| + |B| = n$, there is a vertex $z$ not in $A \cup B$ joined to each
vertex of $A$ and no vertex of $B$. Few explicit families of $n$-e.c. are known
for $n > 2$. In this short note, we give a new construction of 3-e.c. graphs
using the notion of quadrance in the finite Euclidean space $\mathbbm{Z}_p^d$.
