let A={1,2,3...,N} and B1,B2,B3..,Bn be a series of subsets of A which satisfied that |Bi|=m |Bi∩Bj|<=k. what is the maximum of n? (k< m< N)

it can be easily showed that n⩽ [C(N−1,k)/C(m−1,k)]/[N/m] (by counting twice,[X] is integer part of x)

I wonder is there any reserch that tackle this problem? Do we have some profound result?