On limits of dense packing of equal spheres in a cube

We examine packing of n congruent spheres in a cube when n is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of [p3/2] spheres. For this family of packings, the previous best-known arrangements were usually derived from a ccp by Omission of a certain number of spheres without changing the initial structure. In tins paper, we show that better arrangements exist. for all n <= [p(3)/2]-2. We introduce an optimization method to reveal improvements of these packings, and present many new improvements for n <= 1629.