Abstract
There are some results concerning t-designs in which the number of points in the intersection of two blocks takes less than t values. For example, if t = 2, then the design is symmetric (in such a design, v = b or, equivalently, k = r). In 1974, B. Gross described t-(v, k, l) designs that, for some integer s, 0 < s < t, do not contain two blocks intersecting at exactly s points. Below, it is proved that potentially infinite series of designs from the claim of Gross’ theorem are finite. Gross’ theorem is substantially sharpened.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Cameron and J. H. van Lint, Designs, Graphs, Codes, and Their Links (Cambridge. Univ. Press, Cambridge, 1981).
W. O. Alltop, J. Combin. Theory Ser. A 12, 390–395 (1972).
R. Noda, Eur. J. Combin. 22, 91–94 (2001).
P. Hauck, J. Combin. Theor. Ser. A 32, 99–102 (1982).
B. H. Gross, Math. Z. 139, 87–104 (1974).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.A. Makhnev, 2016, published in Doklady Akademii Nauk, 2016, Vol. 470, No. 5, pp. 508–510.
Rights and permissions
About this article
Cite this article
Makhnev, A.A. On extensions of some block designs. Dokl. Math. 94, 563–565 (2016). https://doi.org/10.1134/S1064562416050227
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562416050227