Random sequential packing in Euclidean spaces of dimensions three and four and a conjecture of Palásti

A conjecture of Palásti [11] that the limiting packing density β d in a space of dimension d equals β d where ß is the limiting packing density in one dimension continues to be studied, but with inconsistent results. Some recent correspondence in this journal [7], [8], [13], [14], [15], [16], [18], [19], [20] as well as some other papers indicate a lively interest in the subject. In a prior study [3], we demonstrated that the conjectured value in two dimensions was smaller than the actual density. Here we demonstrate that this is also so in three and four dimensions and that the discrepancy increases with dimension.