{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T13:00:07Z","timestamp":1768482007831,"version":"3.49.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T00:00:00Z","timestamp":1580256000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T00:00:00Z","timestamp":1580256000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1359307"],"award-info":[{"award-number":["1359307"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["319197"],"award-info":[{"award-number":["319197"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006751","name":"U.S. Army","doi-asserted-by":"publisher","award":["W911NF1610008"],"award-info":[{"award-number":["W911NF1610008"]}],"id":[{"id":"10.13039\/100006751","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1814253"],"award-info":[{"award-number":["1814253"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2020,2]]},"DOI":"10.1007\/s10444-020-09745-7","type":"journal-article","created":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T16:02:53Z","timestamp":1580313773000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Universal optimal configurations for the p-frame potentials"],"prefix":"10.1007","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6495-2348","authenticated-orcid":false,"given":"X.","family":"Chen","sequence":"first","affiliation":[]},{"given":"V.","family":"Gonzalez","sequence":"additional","affiliation":[]},{"given":"E.","family":"Goodman","sequence":"additional","affiliation":[]},{"given":"S.","family":"Kang","sequence":"additional","affiliation":[]},{"given":"K. A.","family":"Okoudjou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,29]]},"reference":[{"key":"9745_CR1","unstructured":"Ben Av, R., Goldberger, A., Dula, G., Strassler, Y.: Energy minimization in cpn: some numerical and analytical results, arXiv:1810.04640, preprint (2018)"},{"key":"9745_CR2","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.laa.2015.02.020","volume":"475","author":"A Barg","year":"2015","unstructured":"Barg, A., Glazyrin, A., Okoudjou, K.A., Yu, W.-H.: Finite two-distance tight frames. Linear Algebra Appl. 475, 163\u2013175 (2015)","journal-title":"Linear Algebra Appl."},{"issue":"2-4","key":"9745_CR3","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1023\/A:1021323312367","volume":"18","author":"JJ Benedetto","year":"2003","unstructured":"Benedetto, J.J., Fickus, M.: Finite normalized tight frames. Adv. Comp. Math. 18(2-4), 357\u2013385 (2003)","journal-title":"Adv. Comp. Math."},{"key":"9745_CR4","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/s00041-008-9017-1","volume":"14","author":"JJ Benedetto","year":"2008","unstructured":"Benedetto, J.J., Kebo, A.: The role of frame force in quantum detection. J. Fourier Anal. Appl. 14, 443\u2013474 (2008)","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"9745_CR5","doi-asserted-by":"publisher","first-page":"049850","DOI":"10.1155\/ASP\/2006\/49850","volume":"2006","author":"JJ Benedetto","year":"2006","unstructured":"Benedetto, J.J., Kolesar, J.D.: Geometric properties of grassmannian frames for $\\mathbb {R}^{2}$ and $\\mathbb {R}^{3}$. EURASIP J. Adv. Signal Process. 2006(1), 049850 (2006)","journal-title":"EURASIP J. Adv. Signal Process."},{"issue":"1","key":"9745_CR6","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1090\/proc\/14263","volume":"147","author":"D Bilyk","year":"2019","unstructured":"Bilyk, D., Matzke, R: On the Fejes T\u00f3th problem about the sum of angles between lines. Proc. Am. Math. Soc. 147(1), 51\u201359 (2019)","journal-title":"Proc. Am. Math. Soc."},{"issue":"6","key":"9745_CR7","doi-asserted-by":"publisher","first-page":"1344","DOI":"10.1007\/s00041-015-9408-z","volume":"21","author":"BG Bodmann","year":"2015","unstructured":"Bodmann, B.G., Haas, J.: Frame potentials and the geometry of frames. J. Fourier Anal. Appl. 21(6), 1344\u20131383 (2015)","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"9745_CR8","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.laa.2008.08.002","volume":"430","author":"BG Bodmann","year":"2009","unstructured":"Bodmann, B.G., Paulsen, V.I., Tomforde, M.: Equiangular tight frames from complex Seidel matrices containing cube roots of unity. Linear Algebra Appl. 430(1), 396\u2013417 (2009)","journal-title":"Linear Algebra Appl."},{"key":"9745_CR9","unstructured":"Bukh, B., Cox, C.: Nearly orthogonal vectors and small antipodal spherical codes. arXiv:1803.02949 (2018)"},{"key":"9745_CR10","doi-asserted-by":"crossref","unstructured":"Casazza, P.G., Kutyniok, G.: Introduction to Finite Frames, Finite Frames, Theory and Applications. In: Casazza, P.G., Kutyniok, G. (eds.) , pp 1\u201353. Springer, New York (2013)","DOI":"10.1007\/978-0-8176-8373-3_1"},{"issue":"1","key":"9745_CR11","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s00365-015-9303-5","volume":"43","author":"X Chen","year":"2016","unstructured":"Chen, X., Powell, A.M.: Randomized subspace actions and fusion frames. Constr. Approx. 43(1), 103\u2013134 (2016)","journal-title":"Constr. Approx."},{"issue":"1","key":"9745_CR12","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1090\/S0894-0347-06-00546-7","volume":"20","author":"H Cohn","year":"2007","unstructured":"Cohn, H., Kumar, A.: Universally optimal distribution of points on spheres. J. Amer. Math. Soc. 20(1), 99\u2013148 (2007)","journal-title":"J. Amer. Math. Soc."},{"key":"9745_CR13","first-page":"91","volume":"30","author":"P Delsarte","year":"1975","unstructured":"Delsarte, P., Goethals, J.M., Seidel, J.J.: Bounds for systems of lines, and Jacobi polynomials. Philips Res. Rep. 30, 91\u2013105 (1975)","journal-title":"Philips Res. Rep."},{"key":"9745_CR14","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/BF03187604","volume":"6","author":"P Delsarte","year":"1997","unstructured":"Delsarte, P., Goethals, J. M., Seidel, J. J.: Spherical codes and designs. Geom. Dedicata 6, 363\u2013388 (1997)","journal-title":"Geom. Dedicata"},{"issue":"3","key":"9745_CR15","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1016\/j.jspi.2011.09.001","volume":"142","author":"M Ehler","year":"2012","unstructured":"Ehler, M., Okoudjou, K.A.: Minimization of the probabilistic p-frame potential. J. Statist. Plann. Inference 142(3), 645\u2013659 (2012)","journal-title":"J. Statist. Plann. Inference"},{"issue":"3","key":"9745_CR16","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s11118-008-9075-7","volume":"28","author":"B Farkas","year":"2008","unstructured":"Farkas, B., Nagy, B.: Transfinite diameter, Chebyshev constant and energy on locally compact spaces. Potential Anal. 28(3), 241\u2013260 (2008)","journal-title":"Potential Anal."},{"key":"9745_CR17","unstructured":"Glazyrin, A.: Minimizing the p-frame potential. arXiv:1901.06096 (2019)"},{"issue":"4","key":"9745_CR18","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1109\/MSP.2007.4286567","volume":"24","author":"J Kovacevic","year":"2007","unstructured":"Kovacevic, J., Chebira, A: Life beyond bases: the advent of frames (part i). Signal Process. Mag. IEEE 24(4), 86\u2013104 (2007)","journal-title":"Signal Process. Mag. IEEE"},{"issue":"5","key":"9745_CR19","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1109\/MSP.2007.904809","volume":"24","author":"J Kovacevic","year":"2007","unstructured":"Kovacevic, J: Life beyond bases: The advent of frames (part ii). Signal Process. Mag. IEEE 24(5), 115\u2013125 (2007)","journal-title":"Signal Process. Mag. IEEE"},{"key":"9745_CR20","volume-title":"Finite Frame Theory: A Complete Introduction to Overcompleteness","year":"2016","unstructured":"Okoudjou, K.A (ed.): Finite Frame Theory: A Complete Introduction to Overcompleteness, vol. 73. AMS, Providence (2016)"},{"key":"9745_CR21","unstructured":"Oktay, O.: Frame quantization theory and equiangular tight frames. Ph. D thesis, University of Maryland (2007)"},{"issue":"3","key":"9745_CR22","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/0001-8708(84)90022-7","volume":"52","author":"PD Seymour","year":"1984","unstructured":"Seymour, P.D., Zaslavsky, T: Averaging sets: a generalization of mean values and spherical designs. Adv. Math. 52(3), 213\u2013240 (1984)","journal-title":"Adv. Math."},{"key":"9745_CR23","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/S1063-5203(03)00023-X","volume":"14","author":"T Strohmer","year":"2003","unstructured":"Strohmer, T., Heath, R.W. Jr: Grassmannian frames with applications to coding and communications. Appl. Comp. Harm. Anal. 14, 257\u2013275 (2003)","journal-title":"Appl. Comp. Harm. Anal."},{"key":"9745_CR24","unstructured":"The Sage Developers: Sagemath, the Sage Mathematics Software System (Version 8.2), https:\/\/www.sagemath.org (2018)"},{"key":"9745_CR25","first-page":"10","volume":"37","author":"B Venkov","year":"2001","unstructured":"Venkov, B.: R\u00e9seaux et designs sph\u00e9riques. R\u00e9seaux euclidiens, designs sph\u00e9riques et formes modulaires 37, 10\u201386 (2001)","journal-title":"R\u00e9seaux euclidiens, designs sph\u00e9riques et formes modulaires"},{"key":"9745_CR26","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1109\/TIT.1974.1055219","volume":"20","author":"LR Welch","year":"1974","unstructured":"Welch, L.R.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inform. Theory IT- 20, 397\u2013399 (1974)","journal-title":"IEEE Trans. Inform. Theory IT-"},{"key":"9745_CR27","doi-asserted-by":"crossref","unstructured":"Xu, Z., Xu, Z.: The minimizers of the p-frame potential, arXiv:1907.10861, preprint (2019)","DOI":"10.1016\/j.acha.2020.04.003"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-020-09745-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-020-09745-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-020-09745-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:15:40Z","timestamp":1611792940000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-020-09745-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,29]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["9745"],"URL":"https:\/\/doi.org\/10.1007\/s10444-020-09745-7","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,29]]},"assertion":[{"value":"9 February 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"4"}}