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Abstract:
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E-and MV-optimal block designs for three treatments (1, 2, 3) in b=3n+1 and 3n -1 blocks of size three are identified for all n >= 1 in block effects model when intrablock observations are correlated. A design having n copies of the blocks (1, 2, 3), (2, 3, 1), (3, 1, 2) and one copy of (1, 2, 3)is found to be E- and MV-optimal in the class of all equireplicate connected designs for all positive correlations. The above design is E-optimal in the unrestricted class of all connected designs for all small positive correlations but for large positive correlations, unequally replicated design having n copies of the block (2, 1, 2) and 2n +1 copies of the block (1, 3, 2) is E-optimal. A design having n-1 copies of the blocks (1, 2, 3), (2, 3, 1), (3, 1, 2) and one copy of (1, 2, 3), (3, 1, 2) is E-optimal in the class of all designs for all positive correlations.
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