Golden ratios in a pairs covering problem

Let A"n = {1,...,n} and let B = {B"1,...,B"r} where B"1,...,B"r are subsets of A"n, each of size m. We say that B covers all the pairs (i, j), 1==12n. It is further shown that in this range N(m, n) is a function of the fraction m/n only. Significant results for m<12n are also given.