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arXiv · 1410.7437

Pairwise balanced designs covered by bounded flats

Nicholas M. A. Benson·Peter J. Dukes
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Abstract

We prove that for any $K$ and $d$, there exist, for all sufficiently large admissible $v$, a pairwise balanced design PBD$(v,K)$ of dimension $d$ for which all $d$-point-generated flats are bounded by a constant independent of $v$. We also tighten a prior upper bound for $K = \{3,4,5\}$, in which case there are no divisibility restrictions on the number of points. One consequence of this latter result is the construction of latin squares `covered' by small subsquares.

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Nicholas M. A. Benson, Peter J. Dukes. 2014-10-27. Pairwise balanced designs covered by bounded flats. https://arxiv.org/abs/1410.7437

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