TY  - BOOK
AU  - Ge, Gennian
AU  - Grüttmüller, Martin
AU  - Hartmann, Sven
AU  - Rees, Rolf S.
PY  - 2005
DA  - 2005//
TI  - Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3
T3  - Preprints aus dem Institut für Mathematik
CY  - Germany; Rostock
AB  - A mandatory representation design MRD(K;v) is a pairwise balanced design on v Points with block sizes from the set K in which for each k ∈ K there is at least one block in the design of size k. In this paper, we Show that the necessery criteria for an MRD(K;v) to exist are asymptotically sufficient for finite K. Furthermore, we consider MRDs with K = {4,k}, where k ≡ 2 mod 3, k ≥ 5. Here, we prove that the necessary conditions for existence are sufficient if v ≡ 2 mod 3 and v ≥ 18k^2, or v ≡ 0 mod 3 and v ≥ 12k^3, or v ≡ 1 mod 3 and v ≥ 8k^4.<eng>
UR  - https://purl.uni-rostock.de/rosdok/id00005899
UR  - https://doi.org/10.18453/rosdok_id00005899
DO  - 10.18453/rosdok_id00005899
LA  - English
N1  - Gennian Ge, Martin Grüttmüller, Sven Hartmann, Rolf Rees
ID  - 1987262360
ER  -