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 128/45 ? 2.8444 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.

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 128/45 ? 2.8444 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.