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In this paper, we prove a volume growth estimate for steady gradient Riccisolitons with bounded Nash entropy. We show that such a steady gradient Riccisoliton has volume growth rate no smaller than $r^{\frac{n+1}{2}}.$ This resultnot only improves the estimate in [CMZ21b, Theorem 1.3], but also is optimalsince the Bryant soliton and Appleton's solitons [Ap17] have exactly thisgrowth rate.

An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons