Bin packing in multiple dimensions

I mentioned in a previous column [22] that the best known lower bound for the two-dimensional online bin packing problem is 1.907 by Blitz, van Vliet, Woeginger [2], which is an unpublished (and now lost [24]) manuscript. I have realized since then that even the penultimate result, 1.856, was published only in Andre van Vliet's Ph.D. thesis [23] and is not readily available. It therefore seems like a good idea to describe his methods here, though not in full detail. This will include a discussion of the three-dimensional case. I will also survey other results in multidimensional packing, that were left out in my previous column.