Stevens–Meagher uniform covering array conjecture

A covering array $\operatorname{CA}(N,k,v)$ is an array with $N$ rows, $k$ columns, and entries from an alphabet of size $v$, such that every choice of two columns contains every ordered pair of symbols in at least one row. A covering array is uniform if, in each column, the numbers of occurrences of any two symbols differ by at most $1$. Stevens–Meagher's uniformity conjecture. If there exists a covering array $\operatorname{CA}(N,k,v)$, then there also exists a uniform covering array $\operatorname{CA}(N,k,v)$. The conjecture asserts that an optimal covering array can always be chosen uniformly, and was formulated in 2005. The paper notes that it holds for all known optimal covering arrays, while an analogous uniformity conjecture for covering and packing codes has been disproved; the constrained covering-array analogue studied here can nevertheless force non-uniformity.