New lower bounds for the maximal determinant problem

William P. Orrick , Bruce Solomon , Roland Dowdeswell , Warren D. Smith

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classification 🧮 math.CO

keywords determinantrecordsdimensionsmatricesmaximalalongattainsbeat

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We report new world records for the maximal determinant of an n-by-n matrix with entries +/-1. Using various techniques, we beat existing records for n=22, 23, 27, 29, 31, 33, 34, 35, 39, 45, 47, 53, 63, 69, 73, 77, 79, 93, and 95, and we present the record-breaking matrices here. We conjecture that our n=22 value attains the globally maximizing determinant in its dimension. We also tabulate new records for n=67, 75, 83, 87, 91 and 99, dimensions for which no previous claims have been made. The relevant matrices in all these dimensions, along with other pertinent information, are posted at http://www.indiana.edu/~maxdet \.

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