Top : Science : Math : Combinatorics :
Design Theory
Categories
| Matroids Software |
Websites
Classification of Hadamard matrices and designs.
site exerpt
Ted Spence's Home Page My research interests at the present time are in the area of classification of combinatorial designs of various different sorts. In some cases I have been able to classify the designs completely and where this has been possible I have...Compiled by Jennifer Seberry.
site exerpt
Library of D-optimal designs Only the following orders for n Created 22 October, 1999. Updated 10th November 1999. Please email questions or comments to j.seberry@uow.edu.au...Links to resources for design theory maintained by Peter Cameron.
site exerpt
Design Resources This page includes pointers to Web-based resources for design theory and related parts of discrete mathematics and statistics (coding theory, finite geometry, combinatorics, graph theory We need your help. Please email me (p.j.cameron(at)qmul.ac.uk) to suggest websites which should be included...Links compiled by Peter Cameron.
site exerpt
Design theory: Notes on the Web This list gives you access to lecture notes in design theory, finite geometry and related areas of discrete mathematics on the Web. I have given a brief annotation and table of contents for each set of notes. Note on formats:...A research project founded by the UK Engineering and Physical Sciences Research Council.
site exerpt
DesignTheory.org Python package for computing with combinatorial and statistical designs. This is the official website of a research project funded by the U.K. Engineering and Physical Sciences Research Council to provide various resources for Design Theory through the Internet. The project...Home page for The CRC Handbook of Combinatorial Designs.
site exerpt
Handbook of Combinatorial Designs Welcome to the home page for The CRC Handbook of Combinatorial Designs (ISBN: 0-8493-8948-8 The following pages are currently available. Table of Contents Acknowledgments New Results. These are results that have appeared since the Handbook was sent to press. Errata...With programs and algorithms for creating designs for statistical experiments.
http://lib.stat.cmu.edu/designs/
A database of good covering designs constructed by Dan Gordon.
site exerpt
La Jolla Covering Repository Each of these coverings gives an upper bound for the corresponding C(v,k,t the smallest possible number of blocks in such a covering design. If it does not have a covering you're interested in, or you know of an improvement, please...Compiled by Jennifer Seberry.
site exerpt
Library of SBIBD Hadamard matrices of order 4k^2 and maximal excess (SBIBD(4k^2,2k^2+k,k^2+k Koukouvinos SBIBD(61,25,10 61.25.10S1 Mario Pavcevic and Ted Spence's inequivalent SBIBD((61,25,10) see Ted Spence's Library List Ted Spence's inequivalent SBIBD((66,26,10) see Ted Spence's Library List Created 22 October, 1999. Updated 16 October...The Steiner system S(5,8,24) explicitly computed by Ashay Dharwadker.
site exerpt
The Witt Design computed by Ashay Dharwadker Golay codewords of weight 8. Witt's original construction of S(5, 8, 24) used the largest of the Mathieu groups, M(24 that turns out to be the automorphism group of the Witt design. The group M(24) was the first sporadic simple...Tables and examples in PG(k-1,q) by Yves Edel.
site exerpt
CAP's Generator matrices for caps Introduction A cap in PG(k-1,q) is a set of points no three of which are collinear. If we write the n points as columns of a matrix we obtain a (k,n)-matrix such that every set of...Construction of orthogonal arrays and covering arrays using permutation groups by George Sherwood.
site exerpt
Construction of Orthogonal Arrays and Covering Arrays Using Permutation Groups An alternate formulation is given for index one orthogonal arrays based on computer searches. Orthogonal arrays in diagonal form, and their elements products, powers, and orders, are derived from first column vectors which result from the searches. Mapping operators relating...As orbits of AG(2,q), PSL(2,2^f) and PGammaL(2,2^f) by Yves Edel.
site exerpt
Some constant weight codes Constant weight codes as orbits of AG2(q) There is a C(38,8,8) consisting of four orbits of length 666 and one of length 333 under AG2(37 the generators, the code) There is a C(41,8,8) consisting of one orbit of length 1640,...Tables of homogeneous coherent configurations by A. Hanaki and I. Miyamoto.
http://kissme.shinshu-u.ac.jp/as/
Leonard Soicher reports on new SOMAs, which are generalisations of mutually orthogonal latin squares.
http://www.maths.qmw.ac.uk/~leonard/soma
A library of over 200 orthogonal arrays maintained by N. J. A. Sloane.
site exerpt
Orthogonal Arrays Comments or contributions of new OA's welcomed. John Stufken, Dean De Cock, Warren Kuhfeld, Hongquan Xu and Yingshan Zhang have kindly contributed a number of orthogonal arrays to this library. Thanks also to Chung-yi Suen for some corrections. Related files:...Hyperovals in Desarguesian Planes and related structures in arbitrary projective planes.
site exerpt
Bill Cherowitzo's Hyperoval Page ...A library of Hadamard matrices maintained by N. J. A. Sloane.
site exerpt
Hadamard Matrices Hadamard matrices of orders n up through 28, and at least one of every order n up through 256. This library is maintained by N. J. A. Sloane, AT&T Shannon Lab, 180 Park Ave, Room C233, Florham Park NJ 07932-0971...The search for optimal Golomb Rulers with 20, 21 and 22 marks.
site exerpt
Golomb Rulers The Search For 20 and 21! Ruler refers to a set of non-negative integers such that no two distinct pairs of numbers from the set have the same difference. Conceptually, this is similar to a ruler constructed in such a way that no two pairs of...List of known {-1,1}-matrices with largest determinant and D-optimal designs.
http://www.indiana.edu/~maxdet
Information on Nested and Orthogonal BIBDs and related topics.
site exerpt
D.H.Rees Home page On first using this web site, or in the event of any difficulty using it, please consult the page which explains what technology the web site uses and what technology it expects from your browser. To see if anything has...Fractional factorial design generator by Marko Boon.
site exerpt
Design Wizard 2.0 Detect Java Version, Plug-in, Web Start and Security Settings You will not be able to save the generated design to a file on your local harddisk else setCookie designwizardversion noplugin new Date(year 1, 1, 1 if (screen.width 800) window.open designWizard/index.html _top else window.open designWizard/index.html designWizard location=no,menubar=no,status=no,toolbar=no,screenX=0,left=0,screenY=0,top=0,fullscreen=no,resizable=true,scrollbars=no,titlebar=no else if (f.designwizardversion[0].checked...Description and theory, with references to additional reading.
http://mathworld.wolfram.com/GolombRuler.html
Table of lengths of shortest known Golomb rulers, counts of optimal and near-optimal rulers, and some Fortran programs for dealing with Golomb rulers.
site exerpt
Golomb rulers This web page is devoted to Golomb rulers. A Golomb ruler is a set of integers (marks) a(1 a(n) such that all the differences a(i)-a(j i j) are distinct. Clearly we may assume a(1)=0. Then a(n) is the length of...Ed Pegg Jr. writes about the history (and future) of Golomb rulers and related concepts.
site exerpt
Math Games: Rulers, Arrays, and Gracefulness Babcock found that the optimal way to set up radio signals involved placing them at fixed points so that all distances between signals were distinct. From that basis, he optimized signals within a minimum bandwidth completely eliminating third order distortion...Detailed, theoretical tutorial with references.
site exerpt
Modular and Regular Golomb Rulers Links to related material References Introduction Golomb rulers derive their name from Professor Solomon Golomb who was one of the first to study their construction in relation to combinatorics, coding theory and communications, where most of their applications lie. Intuitively,...Construction and analysis of comparative experiments at the Horticultural Research Institute.
http://biometrics.hri.ac.uk/experimentaldesigns/website/hri.htm
Describes how invariance transformations can be naturally non-continuous. Example uses a 4x4 array with each array or small square dissected by an hypotenuse to create a diamond shape, when all four are considered as one section. Page includes illustrations and bibliography.
site exerpt
Symmetry is often described as invariance under a group of transformations. An unspoken assumption about symmetry in Euclidean 3-space is that the transformations involved are continuous. Diamond theory rejects this assumption, and in so doing reveals that Euclidean symmetry may...