Maximum Number of Quads

Authors :: Byrapuram, Nikhil
Hwiseo
Choi
Ge, Adam
Ge, Selena
Khovanova, Tanya
Lee, Sylvia Zia
Liang, Evin
Mandal, Rajarshi
Oki, Aika
Wu, Daniel
Yang, Michael
Publication Year :: 2023
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.<br />Comment: 13 pages. 2 tables