Maximum Number of Quads

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.

13 pages. 2 tables