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Randomness testing uses asymptotic properties. Thus, as the length of your input increases the effect you are concerned about will disappear. Specifically, there is no need to convert ternary $1$ or $2-$tuples to binary. If you let $n$ increase you cover the interval $\{0,1,\ldots,3^n-1\}$ and then you convert these integers to binary, paying at most a 1 ...

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