The Improvement of the Bound on Hash Family

@article{Ming2008TheIO,
  title={The Improvement of the Bound on Hash Family},
  author={Xianmin Ming and Jiansheng Yang},
  journal={CoRR},
  year={2008},
  volume={abs/0806.1397}
}
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.