%0 Book
%T Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3
%A Ge, Gennian
%A Grüttmüller, Martin
%A Hartmann, Sven
%A Rees, Rolf S.
%S Preprints aus dem Institut für Mathematik
%D 2005
%C Germany; Rostock
%G English
%F 1987262360
%O Gennian Ge, Martin Grüttmüller, Sven Hartmann, Rolf Rees
%X 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>
%L 510
%9 Text
%R 10.18453/rosdok_id00005899
%U https://purl.uni-rostock.de/rosdok/id00005899
%U https://doi.org/10.18453/rosdok_id00005899