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.
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