Authors: Prawin Arya 1, Anil Kumar 1, Ranjit Kumar Paul2

1Senior Scientist , 2Scientist
Indian Agricultural Statistics Research Institute New Delhi-110012, INDIA

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This research deals with the important question in deciding whether a circulant partial triallel cross (PTC) can be obtained from another PTC by just randomizing (relabelling) the lines. This helps to choose the optimum designs with minimum efforts and supplies the interpretation and solutions to the conjecture of Hinkelmann (1967). Statements and theorems relating to the above-mentioned paper have been critically reviewed and needfully modified. PTC's of size 3N and 4N have been proposed and optimum PTC's for parents N=6 to 20 have also been listed.

A partial triallel cross (PTC) is defined as a sample of all the possible three-way crosses to gather information on the combining abilities of the parents (Hinkelmann 1963, 1965). Hinkelmann (1967) further constructed and analysed PTC's using circulant PBIB designs of Kempthorne (1953). Assuming the N parents having been denoted by i = 1,2,...,N, the triplet (i,j)k stands for a typical three-way cross where i and j are half parents and k is full-parent. Here (i,j)k and (j,i)k are taken equivalent in that the two half-parents are symmetrically placed but k being full parent the triplet (i,k)j is different from earlier two triplets from genetic interpretation. The model for the genetic part of such a cross is .. (Please click on download image to read this full article)

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