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Linear models and D-optimal designs for \(n\equiv 2\) \(\text{mod} 4\). (English) Zbl 0849.62040

Summary: In experimental situations where \(n\) two-level factors are involved and \(n\) observations are taken, the \(D\)-optimal first-order saturated design is an \(n \times n \pm 1\) matrix with the maximum determinant. We discuss this problem for \(n \equiv 2 \bmod 4\), we summarize all the known results, and we give some new \(D\)-optimal designs for \(n = 90\), \(n = 226\) and \(n = 362\).

MSC:

62K05 Optimal statistical designs
62K10 Statistical block designs
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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