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On the Construction of Bibd With λ = 1

Published online by Cambridge University Press:  20 November 2018

Kenneth F. N. Scott*
Affiliation:
Scott and Hart Associates, Ottawa, Ontario
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In the past three decades the problem of generating (balanced incomplete block) designs by difference sets has received much attention. Bose [2] gave the two "fundamental theorems of the method of differences". Bose, Sprott [9], Lehmer [7], Chowla [4], Takeuchi [10] and others have given specific classes of difference sets.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Baer, R., Projectivities with fixed points on every line of the plane, Bull. Amer. Math. Soc. 52, 273286.Google Scholar
2. Bose, R. C., On the construction of balanced incomplete block designs, Ann. Eugenics 9 (1939), 353399.Google Scholar
3. Bruck, R. H., Difference sets in a finite group, Trans. Amer. Math. Soc. 78 (1955), 464481.Google Scholar
4. Chowla, S., A property of biquadratic residues, Proc. Nat. Acad. Sci. India. Sect A. 14 (1944), 4546.Google Scholar
5. Dembowski, P., Finite geometries, Springer-Verlag, New York, 1968.Google Scholar
6. Hoffmann, A. J., Cyclic affine planes, Canad. J. Math. 4 (1952), 295301.Google Scholar
7. Lehmer, E., On residue difference sets, Canad. J. Math. 5 (1953), 425432.Google Scholar
8. Singer, J., A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc. 43 (1938), 377385.Google Scholar
9. Sprott, D. A., Some series of balanced incomplete block designs, Canad. J. Math. 7 (1955), 369381.Google Scholar
10. Takeuchi, K., On the construction of a series of BIB designs, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs. 10 (1963), p. 48.Google Scholar
11. Vajda, S., Patterns and configurations infinite spaces, Charles Griffin, London, 1967.Google Scholar