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Small designs for path-connected spaces and path-connected homogeneous spaces


Author: Daniel M. Kane
Journal: Trans. Amer. Math. Soc. 367 (2015), 6387-6414
MSC (2010): Primary 05B30
DOI: https://doi.org/10.1090/tran/6250
Published electronically: April 16, 2015
MathSciNet review: 3356941
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Abstract: We prove the existence of designs of small size in a number of contexts. In particular our techniques can be applied to prove the existence of $ n$-designs on $ S^{d}$ of size $ O_d(n^{d}\log ^{d-1}(n))$.


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Additional Information

Daniel M. Kane
Affiliation: Department of Mathematics, Stanford University, Building 380, Stanford, California 94305
Address at time of publication: Department of Computer Science and Engineering/Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093
Email: dankane@math.stanford.edu, dakane@ucsd.edu

DOI: https://doi.org/10.1090/tran/6250
Received by editor(s): June 27, 2012
Received by editor(s) in revised form: June 28, 2013
Published electronically: April 16, 2015
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.