Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3 Ge, Gennian (VerfasserIn) Grüttmüller, Martin , 1970- (VerfasserIn) Hartmann, Sven , 1969- (VerfasserIn) Rees, Rolf S. , 1960- (VerfasserIn) Text Text 2005 2005 eng electronic resourceremoteComputermedienOnline-Ressource1 Online-Ressource (22 Seiten) 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> Open Access Urheberrechtsschutz 1.0 Gennian Ge, Martin Grüttmüller, Sven Hartmann, Rolf Rees 510 https://purl.uni-rostock.de/rosdok/id00005899 Mandatory representation design mrd (4,k;v) with k--(DE-627)488258820 urn:nbn:de:gbv:28-rosdok_id00005899-8 doi: 10.18453/rosdok_id00005899 oclc: 1621946006 ppn: (DE-627)1987262360