In the answer to Open problems in Euclidean geometry? , Alexey Ustinov brings into attention to a 2012 article.

Greg Aloupis, Robert A. Hearn, Hirokazu Iwasawa, Ryuhei Uehara, Covering Points with Disjoint Unit Disks, 24th Canadian Conference on Computational Geometry (2012)

The abstract of that article confirms that it's concerned of the same problem, and gives improved bounds.

We consider the following problem. How many points must be placed in the plane so that no collection of disjoint unit disks can cover them? The answer, k, is already known to satisfy 11 ≤ k ≤ 53. Here, we improve the lower bound to 13 and the upper bound to 50. We also provide a set of 45 points that apparently cannot be covered, although this has been determined via computer search.

The article also claims that the lower bound of 11 was published in 2008

In the answer to Open problems in Euclidean geometry? , Alexey Ustinov brings into attention to a 2012 article.

Greg Aloupis, Robert A. Hearn, Hirokazu Iwasawa, Ryuhei Uehara, Covering Points with Disjoint Unit Disks, 24th Canadian Conference on Computational Geometry (2012)

The abstract of that article confirms that it's concerned of the same problem, and gives improved bounds.

We consider the following problem. How many points must be placed in the plane so that no collection of disjoint unit disks can cover them? The answer, k, is already known to satisfy 11 ≤ k ≤ 53. Here, we improve the lower bound to 13 and the upper bound to 50. We also provide a set of 45 points that apparently cannot be covered, although this has been determined via computer search.

The article also claims that the lower bound of 11 was published in 2008