Maximum Number of Quads

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Rajarshi Mandal, Tanya Khovanova

Published: 31 Mar 2024, Last Modified: 25 Jan 2026Intelligence Planet Journal of Mathematics and Its ApplicationsEveryoneCC BY 4.0
Abstract: We study the maximum number of quads among $\ell$ cards from an EvenQuads deck of size $2^n$. This corresponds to enumerating quadruples of integers in the range $[0,\ell-1]$ such that their bitwise XOR is zero. In this paper, we conjecture a formula that calculates the maximum number of quads among $\ell$ cards.