For integers n>2 and k>0, an (n×n)?k semi-Latin square is n×n array of k-subsets (called blocks) nk-set (of treatments), such that each treatment occurs once in row column the array. A uniform if every pair blocks, not same or column, intersect positive number treatments. It known a Schur optimal class all squares, here we show when exists, squares are precisely ones. We then compare using crit...

In this paper, we present new infinite families of three and four variable orthogonal designs based on several constructions derived from complementary sequences. The above method leads to the construction of many classes of orthogonal designs. In addition, we obtain new infinite families of weighing matrices constructed by complementary sequences, such as W (144 + 4s, 144) and W (224 + 4s, 196...

A result of Robinson states that no OD(n; 1, 1, 1, 1, 1, n− 5) exists for n > 40. We complement this result by showing the existence of OD(n; 1, 1, 1, 1, 1, n− 5) for n = 32, 40. This includes a resolution to an old open problem regarding orthogonal designs of order 32 as well. We also obtain a number of new orthogonal designs of order 32.

A range of methods is presented for the recursive construction of sets of orthogonal balanced incomplete block designs. To enable these methods, some new types of designs are de1ned. Some examples of these are given, and pairs of orthogonal BIBDs constructed for k =3; =2, for all but 12 values of v where v ≡ 0; 1 (mod 3) with v¿ 6. c © 2002 Elsevier Science B.V. All rights reserved.

A multi-structured design is a block design whose blocks have further structure like partitions, orders, arrays, etc. This problem have strong relationship to combinatorial arrays like orthogonal arrays, balanced arrays, and also many types of sequence problems, optical orthogonal codes, frequency hopping sequences, comma-free codes, etc. There are many different names of block designs which ha...

Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on Latin hypercube designs, including several new designs.

Some constructions of balanced arrays of strength two are provided by use of rectangular designs, group divisible designs, and nested balanced incomplete block designs. Some series of such arrays are also presented as well as orthogonal arrays, with illustrations. # 2002 Wiley Periodicals, Inc. J Combin Designs 10: 303–312, 2002; Published online in Wiley InterScience (www.interscience.wiley.co...

In this correspondence, we present a systematic and closed form construction of complex orthogonal spacetime block codes from complex orthogonal designs of rates (k+1)=2k for 2k 1 or 2k transmit antennas for any positive integer k.

Foldover is a widely used procedure for selecting follow-up experimental runs. As foldover designs require twice as many runs as the initial design, they can be inefficient if the number of effects to be dealiased is smaller than the size of the original experiment. Semifolding refers to adding half of a foldover fraction and is a technique that has been investigated in recent literature for re...

Abstract Metal hydride offers an efficient and cost-effective method to store hydrogen. In this study, Taguchi coupled with grey relational analysis was used optimize the design parameters i.e., diameter of helical tube (d h ), major m number turns (N) velocity heat transfer fluid ( V f ) for exchanger embedded inside metal bed achieve minimum desorption time (t d 80% outlet temperature (T 0 (H...