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In this paper, we prove that the number   $B(p,g)$   of isomorphism classes of abelian varieties over a prime field   $\mathbb{F}_p$   of dimension   $g$   has a lower bound   $p^{\frac{1}{2}g^2(1+o(1))}$   as   $g \rightarrow \infty$  . This is the 1st nontrivial result on the lower bound of   $B(p,g)$  . We also improve the upper bound   $2^{34g^2}p^{\frac{69}{4} g^2 (1+o(1))}$   of   $B(p,g)$   given by Lipnowski and Tsimerman [  7 ] to   $p^{\frac{45}{4} g^2(1+o(1))}$  .

On the Lower Bound of the Number of Abelian Varieties Over 𝔽 p