Balanced nine-variable Boolean function of nonlinearity 242

Determine whether there exists a balanced nine-variable Boolean function with nonlinearity 242.

Background

The paper proves that the maximum nonlinearity of nine-variable Boolean functions is 242 and notes that known examples attaining this value are not balanced. It therefore leaves unresolved whether the same optimal nonlinearity can be achieved by a balanced Boolean function.

References

Since the known 9-variable functions with nonlinearity 242 are not balanced, it is still an open problem to determine whether there exists a balanced 9-variable Boolean function with nonlinearity 242, which could be further considered in the future.

— The Covering Radius of the Reed--Muller Code RM(1,9) is 242  (2610.17871 - Wang et al., 13 Oct 2026) in Section 6, Conclusions