Maximal resolvable packings and minimal resolvable coverings of triples by quadruples

✍ Scribed by Xiande Zhang; Gennian Ge

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 160 KB
• Volume: 18
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20234

✦ Synopsis

Abstract

Determination of maximal resolvable packing number and minimal resolvable covering number is a fundamental problem in designs theory. In this article, we investigate the existence of maximal resolvable packings of triples by quadruples of order v (MRPQS(v)) and minimal resolvable coverings of triples by quadruples of order v (MRCQS(v)). We show that an MRPQS(v) (MRCQS(v)) with the number of blocks meeting the upper (lower) bound exists if and only if v≡0 (mod 4). As a byproduct, we also show that a uniformly resolvable Steiner system URS(3, {4, 6}, {r~4~, r~6~}, v) with r~6~≤1 exists if and only if v≡0 (mod 4). All of these results are obtained by the approach of establishing a new existence result on RH(6^2__n__^) for all n≥2. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 209–223, 2010