What is the name for this set?

Question

For a fixed alphabet $\Sigma=\{0,\dots,d\}$ $d\geq 1$, a set $A\subseteq \Sigma^n$ contains (non-necessarily binary) strings of length $n$ where for every subset $S=\{i_1,i_2,\dots,i_k\}$ of $k$ string positions, the projection $$ A_{|S}=\{(a_{i1},a_{i2},\dots,a_{ik})|a=(a_1,a_2,\dots,a_n)\in A\} $$ contains all $|\Sigma|^k$ possible strings of length $k$. $A$ is called $(n,k)$-universal set when $|\Sigma|=2$. But what's the general name for the non-binary case? would appreciate any reference.

Answer 1

The general name for this is a Covering Array of strength $k$. A good introduction to the state of art (and some interesting characterizations) is this survey.

Also, $A$ has been called a set with all $k$-projections surjective here.