Pitch tournament designs and other BIBDs—existence results for the case ν = 8n
✍ Scribed by R. Julian R. Abel; Norman J. Finizio; Malcolm Greig; Scott J. Lewis
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 200 KB
- Volume
- 9
- Category
- Article
- ISSN
- 1063-8539
- DOI
- 10.1002/jcd.1015
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
A pitch tournament is a resolvable or near resolvable(ν,8,7) BIBD that satisfies certain criteria in addition to theusual condition that ν ≡ 0 or 1 (mod 8). Here we establish that for the case ν = 8__n__ the necessary condition forpitch tournaments is sufficient for all n > 1615, with at most 187 smaller exceptions. This complements our earlier study of the ν = 8__n__ + 1 case, where we established sufficiency for all n > 224, with at most 28 smaller exceptions. The four missing cases for (ν,8,7) BIBDs are provided, namely ν∈{48,56,96,448}, thereby establishing that the necessary existence conditions are sufficient without exception. Some constructions for resolvable designs are also provided, reducing the existence question for (ν,8,7) RBIBDs to 21 possible exceptions. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 334–356, 2001