Covering the ternary cube by binary subcubes

Peiru Kuang, Yan Wang

For an integer $n\ge 0$, let $f(n)$ be the minimum number of subcubes of ${\mathbb{Z}}_3^n$ of the form $A_1\times \cdots \times A_n$, where $|A_i|=2$ for every $i$, whose union covers…