Some basics of combinatorial block design are combined with certain constraint satisfaction problems of interest to the satisfiability community. The paper shows how such combinations lead to satisfiability problems, and shows empirically that these are some of the smallest very hard satisfiability problems ever constructed. Partially balanced (0; 1) designs (PB01Ds) are introduced as an extens...

Let 1(~j = n, Ai C r5, 1-i -T„ is a partially balanced block design, JAIJ -• • s ~A j . The authors prove that there is such a design for which lA i l = n li2 + O(n lrz`) for some c > 0 . If certain plausible assumptions on the difference of consecutive primes are made, then the above inequality can be improved to lA i l = nV 2 +O((log n)Z ) . It is true that there is a design with HAll > n"'c ...

Linear systematic sampling design is very simple and operationally convenient in practice, but, when the population size is not a multiple of the sample size, results in a variable sample size and in this case sample mean as an estimator of the population mean is not unbiased. To overcome these difficulties and in some cases to increase the efficiency, a number of modifications of linear system...

In [Structural properties and decomposition of linear balanced matrices, Mathematical Programming, 55:129–168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs that do not contain a cycle of length 4 (also known as linear balanced bipartite graphs), and for bal...