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In this paper, Steiner and non-Steiner $2$-$(v,3)$ trades of minimum
volume are considered. It is shown that these trades are composed of a
union of some Pasch configurations and possibly some $2$-$(v',3)$ trades
with $6\leq v'\leq 10$. We determine the number of non-isomorphic
Steiner $2$-$(v,3)$ trades of minimum volume. As for non-Steiner trades the
same thing is done for all $v$, except for $v\equiv 5$ (mod 6).
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