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 $\epsilon-U(N; n, m)$ hash family, in the caes of $n>m^2>1$ and $1\geq\epsilon\geq \epsilon_1(n, m)$, we get that the new bound is better. To $\epsilon-\bigtriangleup U(N; n, m)$ hash family, in the case of $n>m>1$ and $1\geq\epsilon\geq\epsilon_3(n,m)$, the new bound is better. To $\epsilon-SU(N; n, m)$ hash family, in the case of $n>2^m>2$ and $1\geq\epsilon\geq \epsilon_4(n, m)$, we get that the new bound is better

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 2> 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> 2 m> 2 and 1 ≥ ε ≥ ε4(n, m), we get that the new bound is better