We describe a new construction of Boolean functions. A specific instance of
our construction provides a 30-variable Boolean function having
min-entropy/influence ratio to be 128/45β2.8444 which is presently
the highest known value of this ratio that is achieved by any Boolean function.
Correspondingly, 128/45 is also presently the best known lower bound on the
universal constant of the Fourier min-entropy/influence conjecture