?-Resolvable group divisible designs with block size three

2005 ◽  
Vol 13 (2) ◽  
pp. 139-151
Author(s):  
Yan Zhang ◽  
Beiliang Du
Keyword(s):  
Block Size ◽  
Group Divisible Designs ◽  
Group Divisible ◽  
Resolvable Group

Frames with Block Size Four

1992 ◽  
Vol 44 (5) ◽  
pp. 1030-1049 ◽  
Author(s):  
Rolf S. Rees ◽  
Douglas R. Stinson
Keyword(s):  
Group Size ◽  
Block Size ◽  
List Type ◽  
Combinatorial Designs ◽  
Recursive Construction ◽  
Type Number ◽  
Group Divisible Designs ◽  
Group Divisible ◽  
Resolvable Group

AbstractWe 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 ∈ ﹛8,12﹜,h = 36 and u ∈ ﹛7,18,23,28,33,38,43,48﹜,h = 24 or 120 and u ∈ ﹛7﹜,h = 72 and u ∈ 2Z+ U ﹛n : n ≡ 3 mod4 and n ≤527﹜ U ﹛563﹜; or(iii)h ≡ 6mod l2 and u ∈ (﹛17,29,33,563﹜ U ﹛n : n ≡ 3 or 11 mod 12 and n ≤ 527﹜ U ﹛n : n ≡ 7 mod 12 and n ≤ 259﹜), h = 18.Additionally, we give a new recursive construction for resolvable group-divisible designs from frames: if there is a resolvable k-GDD of type gu, a k-frame of type ﹛mg)v where u ≥ m + 1, and a resolvable TD(k, mv) then there is a resolvable k-GDD of type (mg)uv. We use this to construct some new resolvable GDDs with group size three and block size four.

scholarly journals Resolvable group divisible designs with block size 3

1989 ◽  
Vol 77 (1-3) ◽  
pp. 5-20 ◽  
Author(s):  
Ahmed M. Assaf ◽  
Alan Hartman
Keyword(s):  
Block Size ◽  
Group Divisible Designs ◽  
Group Divisible ◽  
Resolvable Group
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