Families of regular designs based on geometries |
| |
Authors: | KA Bush |
| |
Institution: | Washington State University, Pullman, WA 99163, USA |
| |
Abstract: | Recently Bush and Ostrom (1979) settled most of the open questions with respect to inequivalent solutions of a class of semiregular (SR) designs which can be constructed from nets. This paper is a study of the same nature for two families of regular (R) designs derived from finite projective planes. One family presents no problems, but the other which is a ‘double’ family with two parameters is much more difficult. In fact it is here solved only for designs based on planes of orders 3, 4, 5 and 8. Certain general methods exist which are indicated, but we were unable to resolve even the case 7 using this technique.Basically we show the existence of either inequivalent solutions or show there is but one solution settling a number of open cases. In particular for the case λ1 = 2, λ2 = 1 we give new solutions to a number of D(2) designs or group divisible designs with two associate classes which have no repeated blocks in contrast with the published solutions which have this undesirable property for a number of applications. |
| |
Keywords: | Primary 05B05 Secondary 05B20 05B25 Group Divisible Design D(2) Design Isomorphic Solutions Non-Isomorphic Solutions |
本文献已被 ScienceDirect 等数据库收录! |
|