Mandatory representation designs MRD(4,k;v) with k≡2mod3

AbstractA 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 consider MRDs with K={4,k}, where k≡2mod3,k≥5, and prove that the necessary conditions for existence are sufficient if v≡2mod3 and v≥18k2, or v≡1mod3 and v≥12k3, or v≡0mod3 and v≥8k4