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Four pairwise balanced designs

โœ Scribed by E. R. Lamken; W. H. Mills; R. M. Wilson

Book ID
104631080
Publisher
Springer
Year
1991
Tongue
English
Weight
227 KB
Volume
1
Category
Article
ISSN
0925-1022

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โœฆ Synopsis

We construct pairwise balanced designs on 49, 57, 93, and 129 points of index unity, with block sizes 5, 9, 13, aud 29. This completes the determination of the unique minimal finite basis for the PBD-closed set which consists of the integers congruent to 1 modulo 4. The design on 129 points has been used several times by a number of different authors but no correct version has previously appeared in print.

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Let K = {k,, , k,} be a set of block sizes, and let (pr, , p,} be nonnegative numbers with Cy!',,p, = 1. We prove the following theorem: for any E >O, if a (u, K, 1) pairwise balanced design exists and v is sufficiently large, then a (u, K, 1) pairwise balanced design exists in which the fraction