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In this paper it is shown that these designs are intimately related to rotatable arrangements of points of order r in two and three dimensions, respectively. This result is used to construct exact minimax designs for Fourier series regression of all orders and for spherical harmonics regression of orders one and two. Sequential designs and infinite classes of designs depending on only one parameter are given.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1973.tb00977.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:21:20Z","timestamp":1544160080000},"page":"493-500","source":"Crossref","is-referenced-by-count":16,"title":["Minimax Designs for Fourier Series and Spherical Harmonics Regressions : A Characterization of Rotatable Arrangements"],"prefix":"10.1093","volume":"35","author":[{"given":"Lawrence L.","family":"Kupper","sequence":"first","affiliation":[{"name":"University of North Carolina at Chapel Hill"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920471214700_rssb00977-cit-0001","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1214\/aoms\/1177706093","article-title":"Second order rotatable designs in three dimensions","volume":"30","author":"Bose","year":"1959","journal-title":"Ann. 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Statist."},{"volume-title":"The Theory of Spherical and Ellipsoidal Harmonics.","year":"1931","author":"Hobson","key":"2024090920471214700_rssb00977-cit-0005"},{"key":"2024090920471214700_rssb00977-cit-0006","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1214\/aoms\/1177699984","article-title":"Minimax designs in two-dimensional regression","volume":"36","author":"Hoel","year":"1965","journal-title":"Ann. Math. Statist."},{"key":"2024090920471214700_rssb00977-cit-0007","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1214\/aoms\/1177699361","article-title":"Optimal experimental designs","volume":"37","author":"Karlin","year":"1966","journal-title":"Ann. Math. 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