A Lower Bound on the Constant in the Fourier Min-Entropy/Influence Conjecture

12/15/2022

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by   Aniruddha Biswas, et al.

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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.