Designs from cyclotomy
In this note we use the theory of cyclotomy to help us construct initial blocks from which we can develop balanced and partially balanced incomplete block designs. Our main construction method, using unions of cyclotomic classes, gives us upper bounds on m, the number of associate classes of the design, but not exact values for m; we discuss the possible values of m and the circumstances under which m=1, so that the design is in fact balanced.
Unable to display preview. Download preview PDF.
- R.C. Bose and K.R. Nair, Partially balanced incomplete block designs, Sankhya 4 (1938), 337–372.Google Scholar
- Jennifer Seberry Wallis, Some remarks on supplementary difference sets, Colloq. Math. Soc. Janos Bolyai 10. Infinite and finite sets, Keszthely, Hungary, 1973, 1503–1526.Google Scholar