A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

Latin hypercube design is a good choice for computer experiments. In this paper, we construct a new class of Latin hypercube designs with some high-dimensional hidden projective uniformity. The construction is based on a new class of orthogonal arrays of strength two which contain higher strength orthogonal arrays after their levels are collapsed. As a result, the obtained Latin hypercube designs achieve higher-dimensional uniformity when projected onto the columns corresponding to higher strength orthogonal arrays, as well as twodimensional projective uniformity. Simulation study shows that the constructed Latin hypercube designs are significantly superior to the currently used designs in terms of the times of correctly identifying the significant effects.     

Connectedness of Kronecker sum and partial Kronecker row sum of designs

In this paper we discuss connectedness of a design which is a Kronecker sum or a partial Kronecker row sum of any two equi-replicate and equi-block size designs.     

Centered -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

In this paper properties and construction of designs under a centered version of the -discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

     

The enumeration of cyclic mutually nearly orthogonal Latin squares

In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum such that there exists a set of cyclic MNOLS of order for , as well as providing a full enumeration of sets and lists of cyclic MNOLS of order under a variety of equivalences with . This resolves in the negative a conjecture that proposed that the maximum for which a set of cyclic MNOLS of order exists is .     

Existence of weakly pandiagonal orthogonal Latin squares

A weakly pandiagonal Latin square of order n over the number set {0, 1, . . . , n-1} is a Latin square having the property that the sum of the n numbers in each of 2n diagonals is the same. In this paper, we shall prove that a pair of orthogonal weakly pandiagonal Latin squares of order n exists if and only if n ≡ 0, 1, 3 (mod 4) and n≠3.     

Construction of efficient experimental designs under multiple resource constraints

The aim of this paper is twofold. First, we introduce ‘resource constraints’ as a general concept that covers many practical restrictions on experimental design. Second, to compute optimal or near‐optimal exact designs of experiments under multiple resource constraints, we propose a tabu search heuristic related to the Detmax procedure. To illustrate the scope and performance of the proposed method, we chose the criterion of D‐optimality and computed efficient designs for (i) a block model with limits on the numbers of blocks and on the replications of treatments, (ii) a quadratic regression model with simultaneous marginal and cost constraints, and (iii) a non‐linear regression model with simultaneous direct and cost constraints. As we show, the proposed method generates similar or better results compared with algorithms specialized for computing optimal designs under less general constraints. Copyright © 2015 John Wiley & Sons, Ltd.     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.     

Construction of Sudoku designs and Sudoku-based uniform designs

In this paper, an easy and effective construction method of Sudoku designs with any order is provided based on the right shift operator. Based on the constructed Sudoku designs, a class of Sudoku-based uniform designs is constructed. Moreover, the properties of the constructed Sudoku designs and Sudoku-based uniform designs are investigated, it is shown that both the constructed Sudoku designs and Sudoku-based uniform designs are uniform designs in terms of discrete discrepancy.     

一类图设计的构造

设Kv是一个v点完全图,G是一个有限简单图,Kv上的一个图设计G-GD(v)是一个对子(X,B),其中X是Kv的顶点集合,B是Kv的一些与G同构的子图(称为区组)的集合,使得Kv的任意一条边恰出现在B的一个区组中．文中讨论的简单图是C(r)10,即带有一条弦的10长圈(含有11条边),其中r表示弦的两个端点之间的顶点个数,1≤r≤4．给出了C^（r）10-GD(v)的存在谱：v=0,1(mod11)且v≥11．     

Some Hadamard designs with parameters (71,35,17)

Up to isomorphisms there are precisely eight symmetric designs with parameters (71, 35, 17) admitting a faithful action of a Frobenius group of order 21 in such a way that an element of order 3 fixes precisely 11 points. Five of these designs have 84 and three have 420 as the order of the full automorphism group G. If |G| = 420, then the structure of G is unique and we have G = (Frob₂₁ × Z5):Z4. In this case Z(G) = 〈1〉, G′ has order 35, and G induces an automorphism group of order 6 of Z7. If |G| = 84, then Z(G) is of order 2, and in precisely one case a Sylow 2‐subgroup is elementary abelian. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 144–149, 2002; DOI 10.1002/jcd.996     

A survey of orthogonal arrays of strength two

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New symmetric 2-(176,50,14) designs

In this paper, we construct two new symmetric designs with parameters 2-$(176,50,14)$ as designs invariant under certain subgroups of the full automorphism group of the Higman design. One is self-dual and has the full automorphism group of order 11520 and the other one is not self-dual and has the full automorphism group of order 2520.     

Optimal (4up, 5, 1) optical orthogonal codes

By a (ν, k, 1)‐OOC we mean an optical orthogonal code. In this paper, it is proved that an optimal (4p, 5, 1)‐OOC exists for prime p ≡ 1 (mod 10), and that an optimal (4up, 5, 1)‐OOC exists for u = 2, 3 and prime p ≡ 11 (mod 20). These results are obtained by applying Weil's theorem. © 2004 Wiley Periodicals, Inc.     

Construction of uniform designs without replications

A uniform design scatters its design points evenly on the experimental domain according to some discrepancy measure. In this paper all the design points of a full factorial design can be split into two subdesigns. One is called the complementary design of the other. The complementary design theories of characterizing one design through the other under the four commonly used discrepancy measures are investigated. Based on these complementary design theories, some general rules for searching uniform designs through their complementary designs are proposed. An efficient method to check if a design has repeated points is introduced and a modified threshold-accepting algorithm is proposed to search uniform or nearly uniform designs without replications. The new algorithm is shown to be more efficient by comparing with other existing methods. Many new uniform or nearly uniform designs without replications are tabulated and compared.     

Construction of new symmetric designs with parameters (66,26,10)

It is known that there exists only one (Tran van Trung's) design for (66,26,10) up to now. In this article we consider designs for (66,26,10) with the Frobenius group F₃₉ and we prove that there exist (up to isomorphism) exactly 18 such designs. © 1995 John Wiley & Sons, Inc. We characterize the proper t-wise balanced designs t?(v,K,1) for t ? 3, λ = 1 and v ? 16 with at least two block sizes. While we do not examine extensions of S(3,4,16)'s, we do determine all other possible extensions of S(3,K,v)'s for v ? 16. One very interesting extension is an S(4, {5,6}, 17) design. © 1995 John Wiley & Sons, Inc.     

Construction of new symmetric designs with parameters (70,24,8)

This article presents a construction of all symmetric designs with parameters (70,24,8) on which the group E₈ F₂₁ operates so that the automorphism of order 7 operates fixed-point-free. A method based on enumeration of cosets in group is used for the construction.     

Construction of optimal supersaturated designs by the packing method

A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main effects is greater than the number of runs. It has received much recent interest because of its potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed. A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated. Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties.