Further results on large sets of disjoint group-divisible designs with block size three and type 2n41

✍ Scribed by H. Cao; J. Lei; L. Zhu

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 137 KB
• Volume: 11
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.10032

✦ Synopsis

Abstract

Large sets of disjoint group‐divisible designs with block size three and type 2^n^4^1^ were first studied by Schellenberg and Stinson because of their connection with perfect threshold schemes. It is known that such large sets can exist only for n ≡0 (mod 3) and do exist for all odd n ≡ (mod 3) and for even n=24__m__, where m odd ≥ 1. In this paper, we show that such large sets exist also for n=2^k^(3__m__), where m odd≥ 1 and k≥ 5. To accomplish this, we present two quadrupling constructions and two tripling constructions for a special large set called ^*^LS(2^n^). © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 24–35, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10032