Is there a deterministic algorithm to construct $(n,k)$-universal set of minimum size? Let $S\subseteq \{0,1\}^n$, $S$ is a $(n,k)$-universal set if for every subset of indices $I$ of size $k$, projecting $S$ to $I$ yield the $2^k$ binary strings (all the possible strings of $I$). $S$ is of minimum size if there is no other $(n,k)$-universal set $S'$ where $|S'|&lt;|S|$. 

is there a known algorithm to construct a $(n,k)$-universal set in general and of (close-to) minimum size in particular?
Such constructions appear in papers of Seroussi and Bshouty, Alon, and Naor and Naor. See Bshouty for the latest on this topic.