The Improvement of the Bound on Hash Family

In this paper, we study the bound on three kinds of hash family using the Singleton bound. To ε−U(N ;n,m) hash family, in the caes of n > m > 1 and 1 ≥ ε ≥ ε1(n,m), we get that the new bound is better. To ε − △U(N ;n,m) hash family , in the case of n > m > 1 and 1 ≥ ε ≥ ε3(n,m), the new bound is better. To ε − SU(N ;n,m) hash family, in the case of n > 2m > 2 and 1 ≥ ε ≥ ε4(n,m), we get that the new bound is better.