New bounds for perfect k-hashing

Let C\subseteq \{1,\ldots,k\}^n be such that for any k distinct elements of C there exists a coordinate where they all differ simultaneously. Fredman and Koml\'os studied upper and lower bounds on the largest cardinality of such a set C, in particular proving that as n\to\infty, |C|\leq \exp(n k!/k^{k-1}+o(n)). Improvements over... Show more