On maximum parallel classes in packings

DOI10.1016/J.DISC.2022.112947arXiv2202.06311WikidataQ114190519 ScholiaQ114190519MaRDI QIDQ6390980

Ruizhong Wei

Publication date: 13 February 2022

Abstract: The integer $$ is defined to be the maximum number of blocks in any $(v,k)$-packing in which the maximum partial parallel class (or PPC) has size $ho$. This problem was introduced and studied by Stinson for the case $k=3$. Here, we mainly consider the case $k=4$ and we obtain some upper bounds and lower bounds on $$. We also provide some explicit constructions of $(v,4)$-packings having a maximum PPC of a given size $ho$. For small values of $ho$, the number of blocks of the constructed packings are very close to the upper bounds on $$. Some of our methods are extended to the cases $k>4$.

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial aspects of finite geometries (05B25) Combinatorial aspects of packing and covering (05B40) Finite geometry and special incidence structures (51E99)

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