t-Designs with few intersection numbers

t-Designs with few intersection numbers

Pott, A. and M. Shriklande, t-Designs with few intersection numbers, Discrete Mathematics 90 (1991) 215-217. We give a method to obtain new i-designs from t-designs with j distinct intersection numbers if i + j 1 does not exceed t.

A Note on t-designs with t Intersection Numbers

Let X be a finite set of v elements, called points, and let β be a finite family of distinct k-subsets of X , called blocks. Then the pair D = (X ,β) is called a t-design with parameters (v,k,λ) if any t-subset of X is contained in exactly λ members of β. If λi denotes the number of blocks containing i points, i = 0,1,2, . . . , t−1, then λi is independent of the choice of the i points and λi (...

Sets with few Intersection Numbers from Singer Subgroup Orbits

Using a Singer cycle in Desarguesian planes of order q ≡ 1 (mod 3), q a prime power, Brouwer [2] gave a construction of sets such that every line of the plane meets them in one of three possible intersection sizes. These intersection sizes x, y, and z satisfy the system of equations

Block Intersection Numbers of Block Designs Ii

Enumeration of t-Designs Through Intersection Matrices

In this paper, we exploit some intersection matrices to empower a backtracking approach based on Kramer–Mesner matrices. As an application, we consider the interesting family of simple t-ðtþ 8; tþ 2; 4Þ designs, 1 t 4, and provide a complete classification for t 1⁄4 1; 4, as well as a classification of all non-rigid designs for t 1⁄4 2; 3. We also enumerate all rigid designs for t 1⁄4 2. The co...