@preamble{"\def\cprime{$'$} "}


@string{sv = {Springer-Verlag}}


@article{Loeppky2007,
	Author = {Loeppky, J. L. and Sitter, R. R. and Tang, B.},
	Date-Added = {2019-01-31 11:45:08 +0100},
	Date-Modified = {2019-01-31 11:46:27 +0100},
	Journal = {Technometrics},
	Pages = {454-467},
	Title = {Nonregular Designs With Desirable Projection Properties},
	Volume = {49},
	Year = {2007}}

@article{Deng2002,
	Author = {Deng, L.Y. and Tang, B.},
	Date-Added = {2019-01-15 13:18:21 +0100},
	Date-Modified = {2019-01-15 13:19:26 +0100},
	Journal = {Technometrics},
	Pages = {173-184},
	Title = {Design Selection and Classification for Hadamard Matrices using Generalized Minimum Aberration Criteria},
	Volume = {44},
	Year = {2002}}

@book{Colbourn2006,
	Author = {Colbourn, C. J. and Dinitz, J. H.},
	Date-Added = {2019-01-15 10:38:54 +0100},
	Date-Modified = {2019-01-15 10:39:54 +0100},
	Publisher = {CRC Press},
	Title = {Handbook of Combinatorial Designs},
	Year = {2006}}


@misc{wiki:ConferenceMatrix,
	Author = {Wikipedia},
	Note = {[Online; accessed 4-April-2016]},
	Title = {Conference matrix --- Wikipedia{,} The Free Encyclopedia},
	Url = {https://en.wikipedia.org/w/index.php?title=Conference_matrix&oldid=702633334},
	Year = {2016},
	Bdsk-Url-1 = {https://en.wikipedia.org/w/index.php?title=Conference_matrix&oldid=702633334}}

@book{Wu2009,
	Author = {Wu, C.F.J. and Hamada, M.S.},
	Publisher = {Wiley},
	Title = {Experiments: Planning, Analysis and Optimization},
	Year = {2009}}

@article{Angelopoulos2007,
	Author = {Angelopoulos, P. and Evangalaras, H. and Koukouvinos, C. and Lappas, E.},
	Journal = {Metrika},
	Pages = {139--149},
	Title = {An effective step-down algorithm for the construction and the identification of nonisomorphic orthogonal arrays},
	Volume = {66},
	Year = {2007}}

@book{loeppky2004ranking,
	Author = {Loeppky, J.L.},
	Publisher = {Simon Fraser University},
	Series = {Canadian theses on microfiche},
	Title = {Ranking Non-regular Designs},
	Url = {http://books.google.fr/books?id=b7e7oAEACAAJ},
	Year = {2004},
	Bdsk-Url-1 = {http://books.google.fr/books?id=b7e7oAEACAAJ}}

@misc{eigenweb,
	Author = {Ga\"{e}l Guennebaud and Beno\^{i}t Jacob and others},
	Howpublished = {http://eigen.tuxfamily.org},
	Title = {Eigen v3},
	Year = {2010}}

@misc{EendebakOAwww,
	Author = {Eendebak, Pieter Thijs},
	Note = {\url{http://www.pietereendebak.nl/oapage/}},
	Title = {Orthogonal Array page},
	Url = {http://www.pietereendebak.nl/oapage/},
	Year = {2012},
	Bdsk-Url-1 = {http://www.pietereendebak.nl/oapage/}}

@misc{EendebakOApackageResults,
	Author = {P. T. Eendebak},
	Title = {The {O}rthogonal {A}rray package: results},
	Url = {http://www.pietereendebak.nl/oapackage/},
	Year = {2018},
	Bdsk-Url-1 = {http://www.pietereendebak.nl/oapackage/}}

@misc{EendebakDOF,
	Author = {P. T. Eendebak},
	Note = {Technical report 2014007, University of Antwerp, Faculty of Applied Economics},
	Title = {A canonical form for non-regular arrays based on generalized worldlength pattern values of delete-one-factor projections},
	Url = {http://www.pietereendebak.nl/oapage/index.html},
	Year = {2013},
	Bdsk-Url-1 = {http://www.pietereendebak.nl/oapage/index.html}}


@article{Schoen2018dsd,
author = "Schoen, Eric D. and Eendebak, Pieter T. and Goos, Peter",
doi = "10.1214/18-AOS1723",
fjournal = "The Annals of Statistics",
journal = "Ann. Statist.",
month = "04",
number = "2",
pages = "1179--1202",
publisher = "The Institute of Mathematical Statistics",
title = {A Classification Criterion for Definitive Screening Designs},
_url = "https://doi.org/10.1214/18-AOS1723",
volume = "47",
year = "2019"
}

@article{SchoenConferenceEnumeration,
author = "Schoen, Eric D. and Eendebak, Pieter T. and Goos, Peter",
 title={Enumeration and Classi
cation of De
nitive Screening Designs},
 notes={in preparation}
 }

@article{EendebakSO,
	Author = {Pieter T. Eendebak and Eric D. Schoen},
	Doi = {10.1080/00401706.2016.1142903},
	Eprintx = {https://doi.org/10.1080/00401706.2016.1142903},
	Journal = {Technometrics},
	Number = {1},
	Pages = {69-79},
	Title = {Two-Level Designs to Estimate All Main Effects and Two-Factor Interactions},
	_Url = {https://doi.org/10.1080/00401706.2016.1142903},
	Volume = {59},
	Year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1080/00401706.2016.1142903}}

@misc{EendebakOA,
	Author = {P. T. Eendebak},
	Title = {{O}rthogonal {A}rray page},
	Url = {http://www.pietereendebak.nl/oapage/index.html},
	Year = {2012},
	Bdsk-Url-1 = {http://www.pietereendebak.nl/oapage/index.html}}

@misc{EendebakOAevenodd,
	Author = {P. T. Eendebak},
	Title = {{O}rthogonal {A}rray page -- even-odd arrays},
	Url = {http://www.pietereendebak.nl/oapage/index-evenodd.html},
	Year = {2013},
	Bdsk-Url-1 = {http://www.pietereendebak.nl/oapage/index-evenodd.html}}

@techreport{Sartono2010,
	Author = {Sartono B. and Goos P. and Schoen E. D.},
	Number = {4},
	Pages = {794--809},
	Title = {Classification of Three-Level Strength-Three Arrays},
	Volume = {142},
	Year = {2012}}

@article{Eendebak2015,
	Author = {Pieter T. Eendebak and Eric D. Schoen},
	Doi = {10.1080/00401706.2016.1142903},
	Eprintx = {https://doi.org/10.1080/00401706.2016.1142903},
	Journal = {Technometrics},
	Number = {1},
	Pages = {69-79},
	Title = {Two-Level Designs to Estimate All Main Effects and Two-Factor Interactions},
	Url = {https://doi.org/10.1080/00401706.2016.1142903},
	Volume = {59},
	Year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1080/00401706.2016.1142903}}

@article{Balakrishnan2006,
	Author = {Balakrishnan, N. and Yang, Po},
	Journal = {Annals of the Institute of Statistical Mathematics},
	Keywords = {Indicator function; Fractional word length; Generalized resolution; Resolution III * design; Extended word length pattern},
	Number = {3},
	Pages = {609-618},
	Title = {Connections Between the Resolutions of General Two-level Factorial Designs},
	Url = {http://www.google.nl/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCkQFjAA&url=http%3A%2F%2Fwww.ism.ac.jp%2Feditsec%2Faism%2Fpdf%2F058_3_0609.pdf&ei=sWlwT9dKws7xA8HIqb8N&usg=AFQjCNGTucNTjbOx796D92iL4fblFsvG-A&sig2=oQhfbwnRGAOZxWywUx5uSA},
	Urlx = {http://EconPapers.repec.org/RePEc:spr:aistmt:v:58:y:2006:i:3:p:609-618},
	Volume = {58},
	Year = {2006},
	Bdsk-Url-1 = {http://www.google.nl/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCkQFjAA&url=http%3A%2F%2Fwww.ism.ac.jp%2Feditsec%2Faism%2Fpdf%2F058_3_0609.pdf&ei=sWlwT9dKws7xA8HIqb8N&usg=AFQjCNGTucNTjbOx796D92iL4fblFsvG-A&sig2=oQhfbwnRGAOZxWywUx5uSA}}

@article{Block2005,
	Author = {Block, R. and Mee, R.},
	Journal = {Journal of Quality Technology},
	Pages = {282--293},
	Title = {Resolution IV designs with 128 runs},
	Volume = {37},
	Year = {2005}}

@article{Brouwer2006,
	Author = {Brouwer, A.E. and Cohen, A.M. and Nguyen, M.V.M.},
	Day = {01},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {3268--3280},
	Title = {Orthogonal arrays of strength 3 and small run sizes},
	Url = {http://www.sciencedirect.com/science/article/B6V0M-4FPN8DC-2/1/06c24dd6b3b43714f413cfc2aba5327c},
	Volume = {136},
	Year = {2006},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V0M-4FPN8DC-2/1/06c24dd6b3b43714f413cfc2aba5327c}}

@article{Bulutoglu2008,
	Author = {Bulutoglu, D.A. and Margot, F.},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {654--666},
	Title = {Classification of orthogonal arrays by integer programming},
	Volume = {138},
	Year = {2008}}

@article{Chen2004,
	Author = {Hegang H. Chen and Ching-Shui Cheng},
	Journal = {Statistica Sinica},
	Owner = {eendebakpt},
	Pages = {203--215},
	Timestamp = {2012.10.25},
	Title = {ABERRATION, ESTIMATION CAPACITY AND ESTIMATION INDEX},
	Volume = {14},
	Year = {2004}}

@article{Chen1993,
	Author = {Chen, J. and Sun, D.X. and Wu, C.F.J.},
	Journal = {International Statistical Review},
	Pages = {131--145},
	Title = {A catalogue of two-level and three-level fractional factorial designs with small runs},
	Volume = {61},
	Year = {1993}}

@article{ChengX,
	Author = {Ching-Shui Cheng and Robert W. Mee and Oksoun Yee},
	Journal = {Statistica Sinica},
	Masid = {4937031},
	Pages = {105--119},
	Title = {{SECOND ORDER SATURATED ORTHOGONAL ARRAYS OF STRENGTH THREE}},
	Url = {http://www3.stat.sinica.edu.tw/statistica/oldpdf/A18n13.pdf},
	Volume = {18},
	Year = {2008},
	Bdsk-Url-1 = {http://www3.stat.sinica.edu.tw/statistica/oldpdf/A18n13.pdf}}

@article{Cheng1999,
	Author = {Cheng, C.-S. and Steinberg, D. M. and Sun, D. X.},
	Doi = {10.1111/1467-9868.00164},
	Issn = {1467-9868},
	Journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
	Keywords = {Estimation capacity, Resolution, Suspect two-factor interaction, Upper weak majorization, Word length pattern},
	Number = {1},
	Pages = {85--93},
	Publisher = {Blackwell Publishers Ltd.},
	Title = {Minimum aberration and model robustness for two-level fractional factorial designs},
	Url = {https://doi.org/10.1111/1467-9868.00164},
	Volume = {61},
	Year = {1999},
	Bdsk-Url-1 = {https://doi.org/10.1111/1467-9868.00164}}

@article{Clark2001,
	Author = {Clark, J.B. and Dean, A.M.},
	Journal = {Statistica Sinica},
	Pages = {537--547},
	Title = {Equivalence of fractional factorial designs},
	Volume = {11},
	Year = {2001}}

@article{Deng1999,
	Author = {Deng, L.Y. and Tang, B.},
	Journal = {Statistica Sinica},
	Pages = {1071--1082},
	Title = {Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs},
	Volume = {9},
	Year = {1999}}

@article{Schoen2010,
	Author = {Schoen, E.D.},
	Journal = {Journal of Quality Technology},
	Pages = {197--208},
	Title = {Optimum designs versus orthogonal arrays for main effects and two-factor interactions},
	Volume = {42},
	Year = {2010}}

@techreport{Schoen2007,
	Author = {Schoen E.D.},
	Journal = {Quality and Reliability Engineering International},
	Pages = {467--480},
	Title = {All orthogonal arrays with 18 runs},
	Volume = {25},
	Year = {2009}}

@article{Evangelaras2007:18run,
	Author = {Evangelaras, H. and Koukouvinos, C. and Lappas, E.},
	Journal = {Metrika},
	Pages = {31--37},
	Title = {18-run nonisomorphic three level orthogonal arrays},
	Url = {http://ideas.repec.org/a/spr/metrik/v66y2007i1p31-37.html},
	Volume = {66},
	Year = {2007},
	Bdsk-Url-1 = {http://ideas.repec.org/a/spr/metrik/v66y2007i1p31-37.html}}

@article{Evangelaras2006,
	Author = {Evangelaras, H. and Koukouvinos, C. and Lappas, E.},
	Journal = {Journal of Discrete Mathematical Science and Cryptography},
	Pages = {125--132},
	Title = {An efficient algorithm for the identification of isomorphic orthogonal arrays},
	Volume = {9},
	Year = {2006}}

@article{Evangelaras2004,
	Author = {Evangelaras, H. and Georgiou S. and Koukouvinos, C.},
	Journal = {Metrika},
	Pages = {51--73},
	Title = {Evaluation of inequivalent projections of Hadamard matrices of order 24},
	Url = {http://ideas.repec.org/a/spr/metrik/v59y2004i1p51-73.html},
	Volume = {59},
	Year = {2004},
	Bdsk-Url-1 = {http://ideas.repec.org/a/spr/metrik/v59y2004i1p51-73.html}}

@article{Evangelaras2005,
	Author = {H. Evangelaras, H. and Koukouvinos, C. and Dean, A.M. and Dingus, C.A.},
	Journal = {Metrika},
	Pages = {241--257},
	Title = {Projection properties of certain three level orthogonal arrays},
	Url = {http://ideas.repec.org/a/spr/metrik/v62y2005i2p241-257.html},
	Volume = {62},
	Year = {2005} }

@article{Xu2001,
	Author = {Hongquan Xu and C. F. J. Wu},
	Doi = {10.1214/aos/1013699993},
	Issue = {2001},
	Journal = {Annals of Statistics},
	Masid = {16477878},
	Pages = {1066--1077},
	Title = {{Generalized minimum aberration for asymmetrical fractional factorial designs}},
	Volume = {29},
	Year = {2001},
	Bdsk-Url-1 = {https://doi.org/10.1214/aos/1013699993}}

@book{Donev2007,
	Address = {United Kingdom},
	Author = {Donev, {A. N.} and Atkinson, {A. C.} and Tobias, {R. D.}},
	Isbn = {ISBN-13: 978-0-19-929659-0},
	Language = {English},
	Publisher = {Oxford University Press},
	Series = {Oxford Statistical Science Series},
	Title = {Optimum Experimental Designs, with SAS},
	Year = {2007}}

@article{Xiao2012,
	Author = {Lili Xiao and Dennis K. J. Lin and Fengshan Bai},
	Doi = {10.1080/00224065.2012.11917877},
	_Eprint = {https://doi.org/10.1080/00224065.2012.11917877},
	Journal = {Journal of Quality Technology},
	Number = {1},
	Pages = {2-8},
	Publisher = {Taylor \& Francis},
	Title = {Constructing Definitive Screening Designs Using Conference Matrices},
	_Url = {https://doi.org/10.1080/00224065.2012.11917877},
	Volume = {44},
	Year = {2012} }

@article{Elster1995,
	Abstract = {Screening experiments aim to identify the relevant variables within some process potentially depending on a large number of variables. In this paper we introduce a new class of experimental designs called edge designs. These designs allow a model-independent estimate of the set of relevant variables, thus providing more robustness than traditional designs. We give a bound on the determinant of the information matrix of certain edge designs, and show that a large class of edge designs meeting this bound can be constructed from conference matrices. We also show that the resulting conference designs have an optimal space exploration property which guards against unexpected nonlinearities. We survey the existence of and constructions for conference matrices, and, for $n < 50$ variables, give explicit such matrices when n is a prime, and references to explicit constructions otherwise.},
	Author = {Clemens Elster and Arnold Neumaier},
	Issn = {00063444},
	Journal = {Biometrika},
	Number = {3},
	Pages = {589--602},
	Publisher = {[Oxford University Press, Biometrika Trust]},
	Title = {Screening by Conference Designs},
	Url = {http://www.jstor.org/stable/2337536},
	Volume = {82},
	Year = {1995},
	Bdsk-Url-1 = {http://www.jstor.org/stable/2337536}}

@article{Evangelaras2007,
	Author = {H. Evangelaras, H. and Koukouvinos, C. and Lappas, E.},
	Day = {01},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {2080--2086},
	Title = {Further contributions to nonisomorphic two level orthogonal arrays},
	Url = {http://www.sciencedirect.com/science/article/B6V0M-4K5J9J7-1/1/08bcb476489ad92a181fd6de36391bee},
	Volume = {137},
	Year = {2007},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V0M-4K5J9J7-1/1/08bcb476489ad92a181fd6de36391bee}}

@misc{Xu09recentdevelopments,
	Author = {Hongquan Xu and Frederick K. H. Phoa and Weng Kee Wong},
	Journal = {Statist. Surv.},
	Pages = {18--46},
	Title = {Recent developments in nonregular fractional factorial designs},
	Volume = {3},
	Year = {2009}}

@article{Hedayat1997b,
	Author = {Hedayat, A.S. and Seiden, E. and Stufken, J.},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {43--63},
	Title = {On the maximal number of factors and the enumeration of 3-symbol orthogonal arrays of strength 3 and index 2},
	Volume = {58},
	Year = {1997}}

@book{Hedayat1999,
	Author = {Hedayat, A.S. and Sloane, N.J.A. and Stufken, J.},
	Doi = {10.1007/978-1-4612-1478-6},
	Publisher = {Springer},
	Title = {Orthogonal arrays : theory and applications},
	Year = {1999},
	Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4612-1478-6}}

@article{Hedayat1997a,
	Author = {Hedayat, A.S. and Stufken, J. and Su, G.},
	Journal = {Annals of Statistics},
	Pages = {2044--2053},
	Title = {On the construction and existence of orthogonal arrays with three levels and indexes $1$ and $2$},
	Volume = {25},
	Year = {1997}}

@book{Kaski2005,
	Address = {New York, NY, USA},
	Author = {Kaski, P. and \"{O}sterg{\aa}rd, P.R.J.},
	Isbn = {3540289909},
	Publisher = {Springer-Verlag},
	Title = {Classification Algorithms for Codes and Designs},
	Year = {2005}}

@article{Katsaounis2008,
	Author = {Katsaounis, T.I. and Dean, A.M.},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {245--258},
	Title = {A survey and evaluation of methods for determination of combinatorial equivalence of factorial designs},
	Volume = {138},
	Year = {2008}}

@article{LamTonchev,
	Author = {Lam, C. and Tonchev, V.D.},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {187--202},
	Title = {Classification of affine resolvable 2-(27, 9, 4) designs},
	Volume = {56},
	Year = {1996}}

@article{OALattice,
	Author = {Rains, E.M. and Sloane, N.J.A. and Stufken J.},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {477--500},
	Title = {The lattice of $N$-run orthogonal arrays},
	Volume = {102},
	Year = {2002}}

@article{Rao1947,
	Author = {Rao, C.R.},
	Journal = {Journal of the Royal Statistical Society Supplement},
	Pages = {128--139},
	Title = {Factorial experiments derivable from combinatorial arrangements of arrays},
	Volume = {9},
	Year = {1947}}

@article{Ryan2010,
	Abstract = { Xu has cataloged 165 minimum aberration (MA) regular fractional factorial
	(FF) designs with 2-levels and large run sizes N=128 (m=8--64 factors),
	N=256 (m=9--28, 109--119), N=512 (m=10--25, 238--246), N=1024 (m=11--24,
	488--501), N=2048 (m=12--23), and N=4096 (m=13--24). Such an extensive
	catalog was produced because of an improved algorithm. We extend
	the catalog by 36 MA, 2-level regular FF designs: N=256 (m=29--36,
	100--108), N=512 (m=26--29), N=1024 (m=25--28), N=2048 (m=24--32), and
	N=4096 (m=25--26). Although such enumeration problems are notoriously
	difficult with increased N and/or m, we brought the newly solved
	problems within computational reach by changing the vital isomorphism
	check component of Xu's algorithm. Here we present a new, compact
	graph for solving regular design isomorphism problems and use the
	nauty program to solve the corresponding graph isomorphism problems.
	Supplemental appendices are available online. },
	Author = {Ryan, Kenneth J. and Bulutoglu, Dursun A.},
	Doi = {10.1198/TECH.2010.08020},
	Eprint = {\url{http://www.tandfonline.com/doi/pdf/10.1198/TECH.2010.08020}},
	Journal = {Technometrics},
	Number = {2},
	Pages = {250-255},
	Title = {Minimum Aberration Fractional Factorial Designs With Large N},
	Url = {http://www.tandfonline.com/doi/abs/10.1198/TECH.2010.08020},
	Volume = {52},
	Year = {2010},
	Bdsk-Url-1 = {http://www.tandfonline.com/doi/abs/10.1198/TECH.2010.08020},
	Bdsk-Url-2 = {https://doi.org/10.1198/TECH.2010.08020}}

@article{Schoen:18,
	Author = {Schoen, E.D.},
	Journal = {Quality and Reliability Engineering International},
	Pages = {467--480},
	Title = {All orthogonal arrays with 18 runs},
	Volume = {25},
	Year = {2009}}

@inproceedings{Bliss2007,
	Author = {Tommi Junttila and Petteri Kaski},
	Booktitle = {Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithms and Combinatorics},
	Editor = {David Applegate and Gerth St{\o}lting Brodal and Daniel Panario and Robert Sedgewick},
	Optaddress = {New Orleans, LA},
	Optmonth = {January 6},
	Optpublisher = {Society for Industrial and Applied Mathematics},
	Pages = {135--149},
	Publisher = {SIAM},
	Title = {Engineering an efficient canonical labeling tool for large and sparse graphs},
	Year = {2007}}

@article{nautyI,
	Author = {McKay, B.},
	Journal = {Congressus Numerantium},
	Pages = {45--87},
	Title = {Practical Graph Isomorphism},
	Volume = {30},
	Year = {1981}}

@article{nautyII,
	Author = {Brendan D. McKay and Adolfo Piperno},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://arxiv.org/abs/1301.1493},
	Journal = {CoRR},
	Title = {Practical graph isomorphism, II},
	Volume = {abs/1301.1493},
	Year = {2013}}

@article{Eendebak2009,
	Author = {Schoen, Eric D. and Eendebak, Pieter T. and Nguyen, Man V. M.},
	Doi = {10.1002/jcd.20236},
	Issn = {1520-6610},
	Journal = {Journal of Combinatorial Designs},
	Keywords = {experimental design, isomorphism, asymmetric array, symmetric array},
	Number = {2},
	Pages = {123--140},
	Publisher = {Wiley Subscription Services, Inc., A Wiley Company},
	Title = {Complete enumeration of pure-level and mixed-level orthogonal arrays},
	Urlx = {https://doi.org/10.1002/jcd.20236},
	Volume = {18},
	Year = {2010},
	Bdsk-Url-1 = {files/JCDarticleR2.pdf},
	Bdsk-Url-2 = {https://doi.org/10.1002/jcd.20236}}

@article{Schur1917,
	Author = {Schur, J.},
	Journal = {Journal f{\"u}r die reine und angewandte Mathematik},
	Language = {ger},
	Pages = {205-232},
	Title = {{\"U}ber Potenzreihen, die im Innern des Einheitskreises beschr{\"a}nkt sind.},
	Url = {http://eudml.org/doc/149467},
	Volume = {147},
	Year = {1917},
	Bdsk-Url-1 = {http://eudml.org/doc/149467}}

@article{Seiden1966,
	Author = {Seiden, E. and Zemach, R.},
	Journal = {Annals of Mathematical Statistics},
	Pages = {1355--1370},
	Title = {On Orthogonal Arrays},
	Volume = {37},
	Year = {1966}}

@misc{integseq,
	Author = {Sloane, N.J.A.},
	Note = {\url{http://www.research.att.com/~njas/sequences/}},
	Title = {The On-Line Encyclopedia of Integer Sequences}}

@article{Matplotlib,
	Abstract = {Matplotlib is a 2D graphics package used for Python
  for application development, interactive scripting, and
  publication-quality image generation across user
  interfaces and operating systems.},
	Author = {Hunter, J. D.},
	Journal = {Computing In Science \& Engineering},
	Number = {3},
	Pages = {90--95},
	Publisher = {IEEE COMPUTER SOC},
	Title = {Matplotlib: A 2{D} graphics environment},
	Volume = {9},
	Year = 2007}

@book{NumPy2012,
	Author = {{The~{Scipy}~community}},
	Citeulike-Article-Id = {11894772},
	Citeulike-Linkout-0 = {http://docs.scipy.org/doc/numpy/reference/},
	Keywords = {computational-science, free-scientific-software, free-software, python, reference-manual, scipy},
	Posted-At = {2013-01-14 15:27:55},
	Priority = {2},
	Publisher = {SciPy.org},
	Title = {{NumPy Reference Guide}},
	Url = {http://docs.scipy.org/doc/numpy/reference/},
	Year = {2012},
	Bdsk-Url-1 = {http://docs.scipy.org/doc/numpy/reference/}}


@misc{WK19,
	Author = {Warren Kuhfeld},
	Url = {http://support.sas.com/techsup/technote/ts723.html},
	Title = {SAS},
	Year = {2018}}

@misc{HongquanXuOnline,
	Author = {Hongquan Xu },
	Note = {\url{http://www.stat.ucla.edu/~hqxu/nsf/}},
	Title = {DoE.base: Full Factorials, Orthogonal Arrays and Base Utilities for DoE Packages},
	Year = {2018}}

@misc{DoEbase,
	Author = {Ulrike Groemping and Boyko Amarov and Hongquan Xu},
	Url = {https://cran.r-project.org/package=DoE.base},
	Title = {DoE.base: Full Factorials, Orthogonal Arrays and Base Utilities for DoE Packages},
	Year = {2018}}


@misc{Sloanewebsite,
	Author = {Sloane, N.J.A.},
	Url = {http://neilsloane.com/oadir/index.html},
	Title = {A library of orthogonal arrays},
	Year = {2014}}

@article{StufkenTang,
	Author = {Stufken, J. and Tang, B.},
	Journal = {Annals of Statistics},
	Pages = {793--814},
	Title = {Complete enumeration of two-Level orthogonal arrays of strength $d$ with $d + 2$ constraints},
	Volume = {35},
	Year = {2007}}

@techreport{Sun2002,
	Author = {Sun, D.X. and Li, W. and Ye, K.Q.},
	Institution = {Department of Applied Mathematics and Statistics, SUNY at Stony Brook},
	Title = {An algorithm for sequentially constructing nonisomorphic orthogonal designs and its applications},
	Year = {2002}}

@article{Tang2001,
	Abstract = {Deng & Tang (1999) introduced the generalised resolution and minimum
	G&hyphen;aberration criteria for assessing nonregular fractional
	factorials. In Tang & Deng (1999), a relaxed variant of minimum G&hyphen;aberration,
	called minimum G2&hyphen;aberration, is proposed and studied. These
	criteria are defined using a set of J values, called J&hyphen;characteristics.
	In this paper, we show that a factorial design is uniquely determined
	by its J&hyphen;characteristics just as a regular factorial design
	is uniquely determined by its defining relation. The theorem is given
	through an explicit formula that relates the set of design points
	to that of J&hyphen;characteristics. Through this formula, projection
	justification of minimum G2&hyphen;aberration is established.},
	Author = {Tang, Boxin},
	Doi = {10.1093/biomet/88.2.401},
	Institution = {HighWire Press OAI Repository [http://open-archive.highwire.org/handler] (United States)},
	Journal = {Biometrika},
	Keywords = {Articles},
	Location = {http://www.scientificcommons.org/50443059},
	Number = {2},
	Pages = {401-407},
	Publisher = {Oxford University Press},
	Title = {Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration},
	Url = {http://biomet.oxfordjournals.org/cgi/content/short/88/2/401},
	Volume = {88},
	Year = {2001},
	Bdsk-Url-1 = {http://biomet.oxfordjournals.org/cgi/content/short/88/2/401},
	Bdsk-Url-2 = {https://doi.org/10.1093/biomet/88.2.401}}

@article{Tsai2000,
	Author = {Tsai, P.W. and Gilmour, S.G. and Mead, R},
	Journal = {Biometrika},
	Pages = {467--475},
	Title = {Projective three-level main effects designs robust to model uncertainty},
	Volume = {87},
	Year = {2000}}

@article{WangWu,
	Author = {Wang, J.C. and Wu, C.J.F.},
	Journal = {Technometrics},
	Pages = {409--422},
	Title = {Nearly orthogonal arrays with mixed levels and small runs},
	Volume = {34},
	Year = {1992}}

@misc{Xu09algorithmicconstruction,
	Author = {Hongquan Xu},
	Title = {Algorithmic Construction of Efficient Fractional Factorial Designs With Large Run Sizes},
	Year = {2009}}

@article{Xu2005,
	Author = {Xu, H.},
	Journal = {Metrika},
	Pages = {259--281},
	Title = {A catalogue of three-level regular fractional factorial designs},
	Volume = {62},
	Year = {2005}}

@article{Yamamoto1996,
	Author = {Yamamoto, S. and Fujii, Y. and Hyodo, Y. and Yumiba, H.},
	Journal = {Journal of Statistical Planning and Inference},
	Pages = {269--287},
	Title = {New light on fractional $2^m$ factorial designs},
	Url = {http://www.sciencedirect.com/science/article/B6V0M-3SNN2FJ-S/1/520f894d8667adf20b8daa80622cfe3c},
	Volume = {56},
	Year = {1996},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V0M-3SNN2FJ-S/1/520f894d8667adf20b8daa80622cfe3c}}

@article{Ye2008,
	Author = {Ye, K.Q. and Park, D. and Li, W. and Dean, A.M.},
	Journal = {Statistics and Applications},
	Pages = {1--9},
	Title = {Construction and classification of orthogonal arrays with small numbers of runs},
	Volume = {6},
	Year = {2008}}

@article{Ye03indicatorfunction,
	Author = {Kenny Q. Ye and Q. Ye},
	Journal = {Ann. Statist},
	Pages = {984--994},
	Title = {Indicator Function and its Application in Two-level Factorial Designs},
	Volume = {31},
	Year = {2003}}

@misc{rfc1951,
	Author = {P. Deutsch},
	Howpublished = {RFC 1951 (Informational)},
	Month = may,
	Number = {1951},
	Organization = {Internet Engineering Task Force},
	Publisher = {IETF},
	Series = {Request for Comments},
	Title = {{DEFLATE Compressed Data Format Specification version 1.3}},
	Url = {http://www.ietf.org/rfc/rfc1951.txt},
	Year = 1996,
	Bdsk-Url-1 = {http://www.ietf.org/rfc/rfc1951.txt}}

@misc{rfc1952,
	Author = {P. Deutsch},
	Howpublished = {RFC 1952 (Informational)},
	Month = may,
	Number = {1952},
	Organization = {Internet Engineering Task Force},
	Publisher = {IETF},
	Series = {Request for Comments},
	Title = {{GZIP file format specification version 4.3}},
	Url = {http://www.ietf.org/rfc/rfc1952.txt},
	Year = 1996,
	Bdsk-Url-1 = {http://www.ietf.org/rfc/rfc1952.txt}}


