Hiding in the crowd: asympstotic bounds on blocking sets

We consider the problem of blocking all rays emanating from a unit disk U by a minimum number Nd of unit disks in the two-dimensional space, where each disk has at least a distance d to any other disk. We study the asymptotic behavior of Nd, as d tends to innity. Using a regular ordering of disks on concentric circular rings we derive upper and lower bounds and prove that 2 16 Nd d2 2 2 , as d goes to innity.