Abstract
Aλ-setS in a symmetric 2-(v, k, λ) designΠ is a subset which every block meets in 0, 1 orλ points such that for any point ofS there is a unique block meetingS at that point only. Ovoids in three-dimensional projective spaces are examples ofλ-secs. It is shown that ifπ has aλ-set thenπ is a geometroid withv=λu 2+u+1 andk=λu+1, whereu≧λ−1. The cases whenu isλ−1,λ andλ+1 are investigated and some open problems discussed.
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