Construction of some new three associate class partially balanced incomplete block designs in two replicates

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Author
Kipkemoi, E. C.
Koske, J. k.
Mutiso, J. M.
Bekolle, David
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Search for experimental designs which aid in research studies involving
large number of treatments with minimal experimental units has been desired
overtime. This paper constructs some new series of three associate Partially
Balanced Incomplete Block (PBIB) designs having n(n - 2) /4 treatments
with three associate classes in two replicates using the concept of triangular
association scheme. The design is constructed from an even squared array
of n rows and n columns (n _> 8) with its both diagonal entries bearing no
treatment entries and that given the location of any treatment in the squared
array, the other location of the same treatment in the array is predetermined.
The design and association parameters for a general case of an even integer
n >_8 are obtained with an illustrated case for n = 8. Efficiencies of the
designs within the class of designs are obtained for a general case of even n >_8
with a listing of efficiencies of designs with blocks sizes in the interval [8,22].
The designs constructed have three associate classes and are irreducible to
minimum number of associate classes.
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- SIMC 2013 [6]