This paper studies the pseudorandomness of four celebrated binary sequence constructions by several authors (Goubin, Gyarmati, Mauduit, Pethő, Rivat, and Sárközy) based on computational evidence. Furthermore, a new theorem establishes a strong link between the correlation measure and the combined measure: for families of sequences satisfying a certain closure property: low correlation ($C_\ell$) implies a low combined measure ($Q_\ell$). This theoretical result confirms that controlling standard correlation is a powerful method for controlling correlation along arithmetic progressions for broad classes of pseudorandom sequence families. By applying this new theorem, we derive new upper bounds for the combined measure $Q_\ell$ for the established four constructions, thereby confirming their strong combined-measure properties.