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?

let $A=\{1,2,3...,N\}$ and $B_1,B_2,B_3\dots,B_n$ be a series of subsets of $A$ which satisfied that $|B_i|=m$, $|B_i\cap B_j|\le k$. what is the maximum of $n$? ($k< m< N$)

it can be easily showed that $n\le [C(N−1,k)/C(m−1,k)]/[N/m]$ (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?

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?

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?