منابع مشابه
Frames with Block Size Four
We investigate the spectrum for frames with block size four, and discuss several applications to the construction of other combinatorial designs. Our main result is that a frame of type hu, having blocks of size four, exists if and only if u ≥ 5, h ≡ 0 mod 3 and h(u − 1) ≡ 0 mod 4, except possibly where (i) h = 9 and u ∈ {13, 17, 29, 33, 93, 113, 133, 153, 173, 193}; (ii) h ≡ 0 mod 12 and u ∈ {...
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A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. # 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007
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The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.
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A group divisible design is resolvable if there exists a partition n = {P,, Pz, . .} of p such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all A. The case where M = { 1) has been solved by Ray-Chaudhuri and Wilson for I = 1, and by Hanani for all h > 1. The case where M is a s...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2008
ISSN: 1063-8539,1520-6610
DOI: 10.1002/jcd.20166