The number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety

Let $N_g$ be the number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety. We prove that $N_g\sim 2^{g-1}$ as $g\to \mathrm{\infty }$.