Unirationality of the moduli space of genus 36 polarized K3 surfaces

Let $\mathcal{K}_{36}$ denote the moduli space of primitively polarized smooth $\mathrm{K3}$ surfaces of genus $36$. Unirationality conjecture. The moduli space $\mathcal{K}_{36}$ is unirational. This extends the known unirationality results for moduli spaces of polarized $\mathrm{K3}$ surfaces in lower genera; the claim concerns the genus $36$ case studied in the paper.