Some new block designs of dimension three

zbMATH Open1427.05038arXiv1907.08548MaRDI QIDQ5206555

Peter Dukes, Coen del Valle

Publication date: 18 December 2019

Abstract: The dimension of a block design is the maximum positive integer $d$ such that any $d$ of its points are contained in a proper subdesign. Pairwise balanced designs PBD$(v,K)$ have dimension at least two as long as not all points are on the same line. On the other hand, designs of dimension three appear to be very scarce. We study designs of dimension three with block sizes in $K=3,4$ or $3,5$, obtaining several explicit constructions and one nonexistence result in the latter case. As applications, we obtain a result on dimension three triple systems having arbitrary index as well as symmetric latin squares which are covered in a similar sense by proper subsquares.

Full work available at URL: https://arxiv.org/abs/1907.08548

zbMATH Keywords

Latin squaresdimensiontriple systemsblock designsSteiner spaces

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Triple systems (05B07) Combinatorial structures in finite projective spaces (51E20)

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