Infinitely many triangle-minimizing digon-free pseudocircle arrangements

Let $n$ be a positive integer, and let a digon-free intersecting arrangement be an arrangement of $n$ pseudocircles in which every pair intersects and no cell is a digon. Let $p_3(\mathcal{A})$ denote the number of triangular cells of an arrangement $\mathcal{A}$. Triangle-minimization conjecture. There are digon-free intersecting arrangements $\mathcal{A}$ of $n$ pseudocircles satisfying

$$p_3(\mathcal{A})=\left\lceil\frac{4n}{3}\right\rceil$$

for infinitely many values of $n$. The bound $\lceil 4n/3\rceil$ is known and is reported to be attained for $6\leq n\leq14$; the conjecture asks for infinitely many attaining values.