@Book{1987262360,
author="Ge, Gennian
and Gr{\"u}ttm{\"u}ller, Martin
and Hartmann, Sven
and Rees, Rolf S.",
title="Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3",
series="Preprints aus dem Institut f{\"u}r Mathematik",
year="2005",
address="Germany; Rostock",
abstract="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>",
note="Gennian Ge, Martin Gr{\"u}ttm{\"u}ller, Sven Hartmann, Rolf Rees",
doi="10.18453/rosdok_id00005899",
url="https://purl.uni-rostock.de/rosdok/id00005899",
url="https://doi.org/10.18453/rosdok_id00005899",
language="English"
}