Existence of rank 3 Ulrich bundles on Veronese surfaces of odd degree

Let $(\mathbb{P}^2,dH)$ denote the projective plane polarized by $dH$, where $d$ is an odd integer and $d\geq 3$. Rank 3 Ulrich-bundle conjecture. There exists a rank $3$ Ulrich bundle on $(\mathbb{P}^2,dH)$ for all odd degrees $d\geq 3$. The authors verified existence computationally for odd degrees up to $d=43$; the conjecture asserts existence in every odd degree at least $3$.