Incomplete group divisible designs with block size four and general index |
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| Authors: | Li-dong Wang Hai-rong Kong Hong-juan Liu |
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| Affiliation: | [1]Department of Basic Courses, Chinese People＇s Armed Police Force Academy, Langfang 065000, China [2]School of Science, Hebei University of Technology, Tianjin 300401, China [3]Department of Computer Science and Engineering, Langfang Polytechnic Institute, Langfang 065000, China |
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| Abstract: | ![]()
In this paper, we investigate the existence of incomplete group divisible designs (IGDDs) with block size four, group-type (g, h) u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg(u − 1) ≡ 0 (mod 3), λ(g − h)(u−1) ≡ 0 (mod 3), and ⇌u(u − 1)(g 2 − h 2) ≡ 0 (mod 12). These necessary conditions are shown to be sufficient for all λ ≥ 2. The known existence result for λ = 1 is also improved. |
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| Keywords: | group divisible design incomplete group divisible design holy group divisible design |
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