Construction of Balanced Incomplete Block Design: An Application of Galois Field
[1]
Janardan Mahanta, Department of Statistics, University of Chittagong, Chittagong, Bangladesh.
This paper focuses on the application of Galois field to construct the balanced incomplete block design. In GF(7), minimum function has been calculated, hence generate the element of GF(7) and construct mutual orthogonal Latin square (MOLS). Using mutual orthogonal Latin square, balanced incomplete block design has been made.
[1]
Arunachalam, R., Sivasubramanian and Ghosh, D. K. (2016). Construction of efficiency-balanced design using factorial design. Journal of Modern Applied Statistical Methods. 15 (1), 239-254.
[2]
Bayrak, H. and Bulut. H. (2006). On the construction of orthogonal balanced incomplete block designs. Hecettepe Journal of Mathematics and Statistics. 35 (2), 235-240.
[3]
Bose R. C. (1939). On the construction of balanced incomplete block designs, Ann. Eugen. 9, 353-99.
[4]
Bose R. C. and Shrikhande (1959). On the falsity of Euler’s conjecture on the non - existence of two orthogonal Latin squares of order 4n+2, Proc. Natl. Acad. Sci. 45, 734.
[5]
Bose R. C., Shrikhande, S. S. and Parker, E. T. (1960). Further results on the construction of mutually Orthogonal latin squares and falsity of Euluer’s conjecture, Can. J. math 12, 189.
[6]
Connor, W. S. (1952). On the construction of balanced incomplete block designs, Ann. math. Stat. 23, 57-71.
[7]
Das M. N. and Giri, (1986), Design and analysis of experiments, (Second Edition), Wiley Eastern Publications Limited, New Delhi.
[8]
Fisher, R. A. (1940). An examination of possible different solutions of a problem incomplete block design, Ann. Eugen. 9, 353-400.
[9]
Kshirsagar, A. M. (1958). A note on incomplete block designs, Ann. math. stat 29, 907-10.
[10]
Mann, H. B. (1942). Constructions of Orthogonal Latin squares, Ann. math. stat 13, 418.
[11]
Menon, P. K. (1961). Method of constructing two mutually orthogonal Latin squares of order 3n+1, Sankhya 23, 281-82.
[12]
Nagell, T. (1951). Irreducibility of the Cyclotomic Polynomial. In Introduction to Number Theory (pp. 160-164). New York: Wiley.
[13]
Pachamuthu, P. (2011). construction of mutually orthogonal Latin square and check parameter relationship of balanced incomplete block design. Int. J. of Mathematical Sciences and Applications, 1 (2), 911-922.
[14]
Sharma, P. L. and Kumar, S. (2014). Balanced incomplete block design (BIBD) using Hadamard Rhotrices. International J. Technology. 4 (1). 62-66.