Question
Let $t$ be a positive integer. Prove that, if there exists a Steiner triple system of index 1 having $v$ varieties, then there exists a Steiner triple system having $v^{t}$ varieties (cf. Exercise 33).
Step 1
A Steiner triple system (STS) of order $v$ is a set of $v$ varieties (elements) and a collection of triples (blocks) such that each pair of varieties occurs in exactly one triple. The index of an STS is the number of times each variety occurs in the triples. In Show more…
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