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A Family of Difference Sets

Published online by Cambridge University Press:  20 November 2018

R. G. Stanton  and
D. A. Sprott
R. G. Stanton
Affiliation:
University of Toronto
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A difference set (,D) is defined in (2) as a subset D of k elements in a group of order υ with the following properties :

(1) if x ∊ , x ≠ 1, there are exactly λ distinct ordered pairs (d1d2) of elements of D such that x = 1d2;

(2) if x ∊ , x ≠ 1, there are exactly λ distinct ordered pairs (3d4) of elements of D such that x = 3d4−1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 73 - 77
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Bose, R. C., On the construction of balanced incomplete block designs, Ann. Eugenics, 9 (1939), 353-399.Google Scholar
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3. Hall, Marshall, A survey of difference sets, Proc. Amer. Math. Soc, 7 (1956), 975-986.Google Scholar
4. Sprott, D. A., A Note on balanced incomplete block designs, Can. J. Math., 6 (1954), 341-346.Google Scholar
5. Sprott, D. A., Some series of balanced incomplete block designs, Sankhyā, 17 (1956), 185-192.Google Scholar