Density of Binary Disc Packings: Lower and Upper Bounds

We provide, for any r∈(0,1), lower and upper bounds on the maximal density of a packing in Euclidean plane discs radius 1 r. The are mostly folk, but improve best previously known ones r∈[0.11,0.74]. For many values r, this gives fairly good idea exact maximum density. In particular, we get new intervals r which does not allow more dense that hexagonal equal discs.