2011/12/18 by Richard P. Brent, William Orrick, Brent, Richard P. +7
Decision Sciences · Engineering · Mathematics · #15B34 (Primary) 05A05 #15B35 (Secondary) #Combinatorics (math.CO) #Computation (stat.CO) #F.2.1 #FOS: Computer and information sciences #FOS: Mathematics #Manufacturing Process and Optimization #Optimal Experimental Design Methods #acm:05A05 #acm:15B34 #acm:15B35 #graph theory and CDMA systems #math.CO #msc:05A05 #msc:15B34 #msc:15B35 #stat.CO
paper · pdf · doi:10.48550/arxiv.1112.4160
28 pages, 4 figures
arxiv created 2011/12/18 · openalex publication_date 2011/12/18 · arxiv updated 2015/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A saturated D-optimal design is a +1,-1 square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal. For order 19 we find all inequivalent saturated D-optimal designs with maximal determinant, 230 x 72 x 17, and confirm that the three known designs comprise a complete set. For order 37 we prove that the maximal determinant is 239 x 336, and find a sample of inequivalent saturated D-optimal designs. Our method is an extension of that used by Orrick to resolve the previously smallest unknown order of 15; and by Chadjipantelis, Kounias and Moyssiadis to resolve orders 17 and 21. The method is a two-step computation which first searches for candidate Gram matrices and then attempts to decompose them. Using a similar method, we also find the complete spectrum of determinant values for +1,-1 matrices of order 13.