Ovoids and monomial ovals (Q1906246)

The authors nearly settle the existence problem for transversal designs (or, equivalently, orthogonal arrays) with block size 8 or 9 and index \(\lambda> 1\). There are only 52 possible exceptions left. This is the first general theorem since the corresponding result for block size 7 was proved by \textit{Haim Hanani} [On transversal designs, Combinatorics, Part 1, Proc. Advanced Study Inst., Breukelen, 42-52 (1974; Zbl 0312.05016)].