Abstract

Several constructions of Steiner triple systems (STS) with ovals are given. For every v ≡ 3 or 7 mod 12 there are STS's with hyperovals, for every v ≡ 1 or 3 mod 6 there are STS's with ovals, and for infinitely many v ≡ 1 or 3 mod 6 there are STS's without ovals. The ovals may be classified by their complementary sets, the so-called counterovals. Several questions remain open.

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