= Synthematic construction of the small Witt design
On a six-point set $X$ and its six <totals of synthemes> $Y$, each duad determines a partition of $Y$ into three pairs according to their shared synthemes. Include both whole halves, the 45 blocks $D\cup(Y\setminus P)$ for these duad-pair incidences, and their complements. For each partition $X=A\sqcup A^c$ into triples, cross synthemes give two triangular components on $Y$; include the four unions of a part of $X$ with a component. These 132 blocks form the <small Witt design>.
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