  We note that a strongly minimal Steiner $k$-Steiner system $(M,R)$ from
(Baldwin-Paolini 2020) can be `coordinatized' in the sense of (Gantner-Werner
1975) by a quasigroup if $k$ is a prime-power. But for the basic construction
this coordinatization is never definable in $(M,R)$. Nevertheless, by refining
the construction, if $k$ is a prime power there is a $(2,k)$-variety of
quasigroups which is strongly minimal and definably coordinatizes a Steiner
$k$-system.
