A comparison of Carlet's second-order nonlinearity bounds
Sihem Mesnager, Gavin McGrew, James A. Davis, Dayton Steele, Katherine Marsten · International Journal of Computer Mathematics · 2015
Carlet provides two bounds on the second-order nonlinearity of Boolean functions. We construct a family of Boolean functions where the first bound (the presumed weaker bound) is tight and the second bound is strictly worse than the first bound. We show that the difference between the two bounds can be made arbitrarily large.