Test of measures of pseudorandom binary sequences

Abstract. In the second half of the 1990's Christian Mauduit and András Sárközy introduced a new quantitative theory of pseudorandomness of binary sequences. Since then numerous papers have been written on this subject and the original theory was generalized in several directions. In this paper, I summarize some of the most notable results in the field. I compare four different constructions in the computational point of view. The first construction is the classic Legendre symbol construction, and the other three are construction based on digits of famous constants such as \(e\), \(\pi\), and \(\sqrt{2}\). I used SAGE, PYTHON, and MATLAB as programming languages. I run multiple tests and calculated the exact values of the pseudorandom measures for each construction in many cases and the runtime are also presented.