A Complete Class of Type 1 Optimal Block Designs with Unequal Replications

  • Sunanda Bagchi
  • John P. MorganEmail author
Original Article


For block designs comparing v treatments in b incomplete blocks of size k, consider settings where bk = vr + 1 and \(r(k-1)=\lambda (v-1)\) for integers r and \(\lambda \). These settings admit designs that possess the symmetry of balanced incomplete block designs and which, though nonbinary, are candidates for optimality in some standard senses. For k = 3, earlier authors have established a class of one binary and one nonbinary design that is complete with respect to all type 1 optimality criteria. Here a solution for the complete class problem for type 1 optimality is obtained for k = 5. The complete class includes two binary and two nonbinary designs.


Block designs Optimality Type 1 criteria Complete class 



This work began when the first author visited the Department of Statistics, Virginia Tech in May, 2016. She expresses her gratitude to everyone in the department for their hospitality during the visit. She also thanks Professor B.V. Rajarama Bhat, professor-in-charge, Stat-Math division, Indian Statistical Institute and Professor Abhyuday Mandal, Department of Statistics, University of Georgia for making this visit possible.

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Theoretical Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia
  2. 2.Department of StatisticsVirginia TechBlacksburgUSA

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