相关论文: Substitutes for the non-existent square lattice de…

Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information…

Let $M(n,d)$ be the maximum size of a permutation array on $n$ symbols with pairwise Hamming distance at least $d$. Some permutation arrays can be constructed using blocks of certain type [2] called product blocks in this paper. We study…

Semi-Latin squares have been extensively studied. They can be interpreted as a special case of latinized block designs where the number of columns is equal to the number of replicates in the design. Latinized row-column designs are…

This paper is about the construction of augmented row-column designs for unreplicated trials. The method uses the representation of a $k \times t$ equireplicate incomplete-block design with $t$ treatments in $t$ blocks of size $k$, termed…

Computational techniques for the construction of quasi-symmetric block designs are explored and applied to the case with $56$ points. One new $(56,16,18)$ and many new $(56,16,6)$ designs are discovered, and non-existence of $(56,12,9)$ and…

We investigate block designs, under the A- and MV-criteria, when each treatment can have only one or two replications due to resource constraints, as can happen, for example, in early generation varietal trials. While these are commonly…

Augmented designs are typically used in early-stage breeding programs to compare single replicates of test entries by combining them with replicated check varieties. One or two dimensional incomplete blocking can be incorporated in the…

Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…

Let X be a tight t-design of dimension n for one of the open cases t=5 or t=7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.

We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong…

We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more…

The dimension of a block design is the maximum positive integer $d$ such that any $d$ of its points are contained in a proper subdesign. Pairwise balanced designs PBD$(v,K)$ have dimension at least two as long as not all points are on the…

It is known since the 1970s that no more than 23 multiplications are required for computing the product of two 3 x 3-matrices. It is not known whether this can also be done with fewer multiplications. However, there are several mutually…

Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs…

Coincidence Site Lattices (CSLs) are a well established tool in the theory of grain boundaries. For several lattices up to dimension $d=4$, the CSLs are known explicitly as well as their indices and multiplicity functions. Many of them…

We compare extensive simulations of QCD with 8 and 12 flavors of degenerate quarks, using the DBW2 gauge action, naive staggered fermions, and the rational hybrid Monte Carlo algorithm. A variety of values of the coupling constant, quark…

Experimental designs that spread out points apart from each other on projections are important for computer experiments when not necessarily all factors have substantial influence on the response. We provide a theoretical framework to…

We introduce an algorithm for computing closure systems derived from a family of implications on a set. Semilattices presentations are explored and used in conjunction with the algorithm to compute various types of lattices freely generated…

An integral lattice which is generated by some vectors of norm $q$ is called $q$-lattice. Classification of 3-lattices of dimension at most four is given by Mimura (On 3-lattice, 2006). As a expansion, we give a classification of 3-lattices…

In this paper we introduce a switching for 2-designs. We illustrate this method by applying it to some symmetric (64,28,12) designs. In that way we obtain six new symmetric (64,28,12) designs. Further, we show that this type of switching…