  Packing a given sequence of items into as few bins as possible in an online
fashion is a widely studied problem. We improve lower bounds for packing boxes
into bins in two or more dimensions, both for general algorithms for squares
and rectangles (in two dimensions) and for an important subclass, so-called
Harmonic-type algorithms for hypercubes (in two or more dimensions). Lastly, we
show that two adaptions of ideas from a one-dimensional packing algorithm to
square packing do not help to break the barrier of 2.
