Complete Enumeration and Properties of Binary Pseudo-Youden Designs PYD(9, 6, 6)

Authors

John P. McSorley, Southern Illinois University CarbondaleFollow
Nicholas C. Phillips, Southern Illinois University Carbondale

Comments

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

Abstract

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.

Recommended Citation

McSorley, John P. and Phillips, Nicholas C. "Complete Enumeration and Properties of Binary Pseudo-Youden Designs PYD(9, 6, 6)." (Apr 2007).