Group‐divisible designs with block size k having k + 1 groups,for k = 4, 5 |
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Authors: | R S Rees |
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Abstract: | We investigate the spectrum for k‐GDDs having k + 1 groups, where k = 4 or 5. We take advantage of new constructions introduced by R. S. Rees (Two new direct product‐type constructions for resolvable group‐divisible designs, J Combin Designs, 1 (1993), 15–26) to construct many new designs. For example, we show that a resolvable 4‐GDD of type g5 exists if and only if g ≡ 0 mod 12 and that a resolvable 5‐GDD of type g6 exists if and only if g ≡ 0 mod 20. We also show that a 4‐GDD of type g4m1 exists (with m > 0) if and only if g ≡ m ≡ 0 mod 3 and 0 < m ≤ 3g/2, except possibly when (g,m) = (9,3) or (18,6), and that a 5‐GDD of type g5m1 exists (with m > 0) if and only if g ≡ m ≡ 0 mod 4 and 0 < m ≤ 4g/3, with 32 possible exceptions. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 363–386, 2000 |
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Keywords: | group‐divisible designs resolvability |
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