Is it true that for every $ϵ>0$ and integer $t\ge 1$, if $N$ is sufficiently large and $A$ is a subset of $[t{]}^N$ of size at least $ϵt^N$ then $A$ must contain a combinatorial line $P$ (a set $P=\{p_1,\dots ,p_t\}$ where for each coordinate $1\le j\le t$ the $j$th coordinate of $p_i$ is either $i$ or constant).