Enumeration of resolvable 2-(10, 5, 16) and 3-(10, 5, 6) designs

✍ Scribed by Luis B. Morales; Carlos Velarde

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 207 KB
• Volume: 13
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20032

✦ Synopsis

Abstract

A backtracking over parallel classes with a partial isomorph rejection (PIR) is carried out to enumerate the resolvable 2‐(10,5,16) designs. Computational results show that the inclusion of PIR reduce substantially the CPU time for the enumeration of all designs. We prove first some results, which enable us to restrict the search space. Since every resolvable 2‐(10,5,16) design is also a resolvable 3‐(10,5,6) design and vice versa, the latter designs are also enumerated. There are 27, 121, 734 such designs with automorphism groups whose order range from 1 to 1,440. From these, designs 2,006,690 are simple. © 2004 Wiley Periodicals, Inc.