Is there a reference about determining the minimum radius of a circle that would cover n circles of radius 1 that are in a square packing configuration ( see Wolfram's MathWorld packing packing description)?
This is a different problem than the "best known packing of equal circles in a circle", though for n=1, 2, and 4 it would have the same result.
For a hexagonal packing configuration, n=1, 2, 3, 7, would have the same result as "best know packing of equal circles in a circle". Believe 6 also does, but would actually cover 7.
If you don't have a square number of small circles, you need to define which ones are missing. It is easy to say "the corners" if you have at least $n^2-4$, but what about if you have $89$ small circles? Asking for the minimum radius is fair.
A partial answer is that if you have a diagonal of $n$ unit circles, the length from one end to the other is $1+(n-1)\sqrt 2$, so the radius of the enclosing circle would be half that. The next layer would be if the farthest center is $n$ units one direction and $m$ units the other from the center (where $n,m$ can both be half integral or integral) the radius is $\frac 12(1+\sqrt{n^2+m^2})$ The minimum is just a constant increase over the size of the circle to contain a given number of lattice points. This is the Gauss circle problem, still unsolved.