Ron Hardin and I did do some work on it, but the most extensive was done in the following papers: MR1600759 (99b:52040) Graham, R. L.; Lubachevsky, B. D.; Nurmela, K. J.; Östergård, P. R. J. Dense packings of congruent circles in a circle. Discrete Math. 181 (1998), no. 1-3, 139--154. (Reviewer: A. Florian) 52C15 (05B40) MR1455513 (98f:52021) Lubachevsky, B. D.; Graham, R. L. Curved hexagonal packings of equal disks in a circle. Discrete Comput. Geom. 18 (1997), no. 2, 179--194. 52C15 (05B40) MR1450127 (98a:52028) Lubachevsky, B. D.; Graham, R. L. Dense packings of $3k(k+1)+1$ equal disks in a circle for $k=1,2,3,4$, and $5$. Computing and combinatorics (Xi'an, 1995), 303--312, Lecture Notes in Comput. Sci., 959, Springer, Berlin, 1995. 52C15 (05B40) etc. Neil
By the way, Kevin Buzzard & I just realized that this M/m problem is (trivially) equivalent to the "Penny Problem": --
Given n non-overlapping* unit disks in the plane, what is the smallest R = R(n) for which they can be arranged inside of a disk of radius R ?
Neil, did you do any numerical work on this question?