Discovery of an Hadamard matrix of order 92

Baumert, L. D.; Golomb, S. W.; Hall, Marshall

doi:10.1090/s0002-9904-1962-10761-7

Cited by 71 publications

(25 citation statements)

References 5 publications

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“…Coxeter showed that compounds of type (1) and (2) (1); the dual compound has type (2). Similarly, given a normalised Hadamard matrix of order m, deleting the first column gives m rows, the vertices of a simplex α m−1 inscribed in γ m−1 , and this leads to a compound of type (3), but in dimension m − 1.…”

Section: Figure 4: a Stella Octangula Inscribed In A Cubementioning

confidence: 99%

Paley and the Paley Graphs

Jones¹

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Section: Figure 4: a Stella Octangula Inscribed In A Cubementioning

confidence: 99%

Paley and the Paley Graphs

Jones¹

2020

Springer Proceedings in Mathematics &Amp; Statistics

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“…Design keys and rules 1 to 3 yield Hadamard matrices for all multiples of 4 up to 152, apart from n = 92 and n = 116. These matrices may be constructed by the four‐square method of Williamson and Baumert, Golomb and Hall, which is given in the succeeding text.…”

Section: Galois Fields and Hadamard Matricesmentioning

confidence: 99%

The Computerized Generation of Fractional‐replicate Designs Using Galois Fields and Hadamard Matrices

Zemroch

2015

Quality & Reliability Eng

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Many statistical programs can now generate fractional‐replicate designs, but most depend on built‐in libraries of experimental plans. Relatively few have design generation algorithms that would give the user true flexibility in the numbers of tests, factors, and factor levels. Powerful search algorithms are now available for generating a wide range of blocked and fractional‐replicate designs using design keys, but these are mostly regular designs with pq units and factors with p, p2, … levels, where p is prime. Many useful classes of irregular design also exist with numbers of units and factor levels which are not powers of p, and the construction rules for most of these use Galois fields and Hadamard matrices in some way. However, the underlying mathematics can be difficult. The aim of this paper is to collate algorithms to expedite the implementation of these structures in software and to present these in an accessible form to a wider community. The use of Galois fields and Hadamard matrices in generating important design classes, such as the fractional 2k Plackett–Burman and sk Addelman–Kempthorne designs, is then detailed. Combining these algorithms with design key searches gives an arsenal of methods that can generate almost all existent balanced fractional‐replicate designs of sizes likely to be used in real‐world experimentation. These methods have all been implemented in the KEYFINDER program, which is available from the author, free of charge. Copyright © 2015 John Wiley & Sons, Ltd.

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“…[Plackett and Burman (1946) provided orthogonal designs for N equal to a multiple of 4 and for all such N I 100 (except 92). The missing N = 92 case was later given by Baumert, Golomb, and Hall (1962).] An advantage of this Plackett and Burman type of approach is that the designs are easy to construct.…”

Section: Small Composite Designsmentioning

confidence: 99%

Small Response-Surface Designs

1990

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Standard composite designs for fitting second-order response surfaces typically have a fairly large number of points, especially when k is large. In some circumstances, it is desirable to reduce the number of runs as much as possible while maintaining the ability to estimate all of the terms in the model. We first review prior work on small composite designs and then suggest some alternatives for k 5 10 factors. In some cases, even minimal-point designs are possible.

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Discovery of an Hadamard matrix of order 92

Abstract: An Hadamard matrix H is an n by n matrix all of whose entries are +1 or -1 which satisfies HH T = n J, H T being the transpose of H. The order n is necessarily 1, 2 or 42, with t a positive integer. R. E. A. C. Paley

Cited by 71 publications

References 5 publications

Paley and the Paley Graphs

Paley and the Paley Graphs

The Computerized Generation of Fractional‐replicate Designs Using Galois Fields and Hadamard Matrices

Small Response-Surface Designs

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