Group divisible designs with two associate classes and \(\lambda_{2}=1\)
Summary: The original classifcation of PBIBDs defined group divisible designs \(\text{GDD}(v = v_1 + v_2 + \dots + v_g, g, k, \lambda_1, \lambda_2)\) with \(\lambda_1 \neq 0\) [cf. \textit{R.C. Bose} and \textit{T. Shimamoto}, ``Classification and analysis of partially balanced incomplete block designs with two associate classes,'' J. Am. Stat. Assoc. 47, 151--184 (1952; Zbl 0048.11603)]. In this paper, we prove that the necessary conditions are suffcient for the existence of the group divisible designs with two groups of unequal sizes and block size three with \(\lambda_2 = 1\).
pairwise balanced incomplete block design
scientific article; zbMATH DE number 5946471