Abstract
Nonuniform group divisible designs (GDDs) have been studied by numerous researchers for the past two decades due to their essential role in the constructions for other types of designs. In this paper, we investigate the existence problem of {4}-GDDs of type gum1 for g≡0mod6. First, we determine completely the spectrum of {4}-GDDs of types 18um1 and 36um1. Furthermore, for general cases, we show that for each g≡0mod6 and g≥12, a {4}-GDD of type gum1 exists if and only if u≥4, m≡0mod3 and 0≤m≤g(u-1)/2, except possibly for g≡6,42,66,78,102,114,138, 174mod180, g≥42 and (u,m){(7,3g-3),(11,5g-9),(11,5g-6),(11,5g-3),(13,6g-9), (13,6g-3)}.
Original language | English |
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Pages (from-to) | 26-52 |
Number of pages | 27 |
Journal | Journal of Combinatorial Designs |
Volume | 22 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2014 |
Externally published | Yes |
Keywords
- double group divisible designs
- group divisible designs
- incomplete group divisible designs
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics