Optimal Packings of 13 and 46 Unit Squares in a Square

Electronic Journal of Combinatorics , 17 (2) (2010), #R126
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r126

Let $s(n)$ be the side length of the smallest square into which $n$ non-overlapping unit squares can be packed. We show that $s(m^2?3)=m$ for $m=4,7$, implying that the most efficient packings of 13 and 46 squares are the trivial ones.