Balanced nested designs and balanced arrays |
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| Affiliation: | 1. Institute of Policy and Planning Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan;2. Department of Mathematics, Faculty of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan;3. Department of Mathematical Sciences, College of Engineering, Osaka Prefecture University, Sakai, Osaka 593-8231, Japan;4. Department of Management Information, Faculty of Informatics, Meisei University, Oume-shi, Tokyo 198-8655, Japan |
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| Abstract: | ![]()
Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric balanced nested balanced incomplete block designs with block size 3 and 4. |
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