Published in Journal of Statistical Planning and Inference, 137(4), 1464-1473. doi: 10.1016/j.jspi.2006.02.011


A binary pseudo -Youden design PYD(9, 6, 6) is a 6 × 6 array in which each cell contains one element from the set V = {1, 2, . . ., 9}, and each element from V occurs 4 times. Every row of the array contains distinct elements and every column contains distinct elements. The rows and columns, when taken together, are pairwise balanced and form a (9, 12, 8, 6, 5)-BIBD. In Preece (1968) and (1976) a total of 345 species of binary PYD(9, 6, 6) were found. Here we complete this enumeration and find 348 species of binary PYD(9, 6, 6). We give a complete set of invariants for these species based upon the numbers of intercalates and anti-intercalates that they contain; and discuss some of their properties. We also show that there are 696 non-isomorphic binary PYD(9, 6, 6), and give a complete set of invariants for these arrays.

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