The sequence of the simple random walks on Hamming schemes $\{H(n, q)\}_{n=1}^{\infty}$ has a cutoff phenomenon for each integer $q$ greater than or equal to $3$. In this paper, for the sequence of simple random walks on Hamming schemes $\{H(n, q)\}_{n=1}^{\infty}$ with $q\geq 3$, we give a simple majorant and a sharp minorant function for total variance distances between transition distributions and stationary distributions.
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