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September, 1977 On Theory and Applications of BIB Designs with Repeated Blocks
W. Foody, A. Hedayat
Ann. Statist. 5(5): 932-945 (September, 1977). DOI: 10.1214/aos/1176343949


Consider BIB designs with parameters $v, b, r, k$ and $\lambda$. Define the support of a BIB design to be the set of its distinct blocks and let the cardinality of the support be $b^\ast$. If $b^\ast < b$ then the design is said to be a BIB design with repeated blocks. Some potential applications of such designs to experimental design and controlled sampling are given. Some necessary and sufficient conditions for the existence of these designs and some algorithms for their constructions are provided. Bounds on $b^\ast$ have been obtained. A necessary and sufficient condition under which a set of blocks can be the support of a BIB design are found. A table of BIB designs with $22 \leqq b^\ast \leqq 56$ for $v = 8$ and $k = 3$ is included.


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W. Foody. A. Hedayat. "On Theory and Applications of BIB Designs with Repeated Blocks." Ann. Statist. 5 (5) 932 - 945, September, 1977.


Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0368.62054
MathSciNet: MR461804
Digital Object Identifier: 10.1214/aos/1176343949

Primary: 62K10
Secondary: 05B05 , 62D05 , 62K05

Keywords: BIB designs with repeated blocks , controlled sampling , support of a BIB design

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 5 • September, 1977
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