Optimally Packing a Large Square by Unit Squares

Abstract

We show that a large square of sidelength $x$ can be packed by unit squares in a manner so that the wasted space $W(x)=O(x^{3/5})$.

This work was extracted from the author's 2024 thesis available at https://unbc.arcabc.ca/dissertations-and-theses/15173 . Since then we have become aware of the 2025 paper arXiv:2508.04603 by Bui that shows a similar result by a different method