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

Aniruddha Biswas; Palash Sarkar

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arXiv · 2212.07713

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

Aniruddha Biswas·Palash Sarkar

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Abstract

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 $128/45 \approx 2.8444$ 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.

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Aniruddha Biswas, Palash Sarkar. 2022-12-15. A Lower Bound on the Constant in the Fourier Min-Entropy/Influence Conjecture. https://arxiv.org/abs/2212.07713

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