Randomness Criteria of the RMT-test Compared to the NIST

In this article, we report a new result of the error limit to be used for the RMT-test, which we have proposed earlier in order to measure the randomness of one-dimensional data sequence based on the comparison to the theoretical value derived by the random matrix theory (RMT). This new limit is obtained by comparing the error level of the RMT-test to the result of the NIST test. We prepared data sequences of various levels of randomness by shuffling a regular sequence many times. The result shows that the RMT error must be less than 0.60% in order to satisfy the requirement of the NIST test. This new limit is severer than the limit that we have obtained in the study of pseudo-random sequences. Although we need to consider the fact that the previous limit was the result of averaging over many samples, and the NIST test is applied only binary sequences and the conditions to apply the two tests are not the same, this result suggests us to reconsider the error limit of the RMT-test in more detail