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June, 1970 The Nonexistence of Linked Block Designs with Latin Square Association Schemes
Peter W. M. John
Ann. Math. Statist. 41(3): 1105-1107 (June, 1970). DOI: 10.1214/aoms/1177696992


The listing of partially balanced linked block designs by Roy and Laha (1957) contains no Latin square designs. The listing of designs with Latin square association schemes by Clatworthy (1956), which includes those given by Bose, Clatworthy and Shrikhande (1954) and by Bose and Shimamoto (1952), and the later listings by Chang and Liu (1964) and by Clatworthy (1967) contain no linked block designs. The question then arises whether any linked block designs exist having the Latin square association scheme. In this note a partial answer to the question is given. It is shown that there do not exist any linked block designs which are partially balanced with two associate classes and have the $L_i$ association scheme for $i = 2,3$ or 4.


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Peter W. M. John. "The Nonexistence of Linked Block Designs with Latin Square Association Schemes." Ann. Math. Statist. 41 (3) 1105 - 1107, June, 1970.


Published: June, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0267.62038
MathSciNet: MR260118
Digital Object Identifier: 10.1214/aoms/1177696992

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 3 • June, 1970
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