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Peer-reviewedCC BY 4.0Mathematics

D-Optimal Saturated Factorial Designs with Three Factors

  • Stavros A. Chatzopoulos1
  1. 1Department of Statistics, School of Economic Sciences, University of Western Macedonia, 51100 Grevena, Greece
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Abstract

The aim of this paper is to study the D-optimal m1×m2×m3, m3≥m2≥m1≥2 saturated factorial designs for estimating the mean and the main effects. A restricted class D of m1×m2×m3 saturated designs is defined. In this class, the upper bounds of the determinant values of D-optimal matrices for the already known 2×m2×m3, m3≥m2≥2, 3×m2×m2, m2≥3, 3×m2×(m2+1), m2≥3 and for 4×4×m3, m3≥4 saturated designs are found. New results regarding the determinant values of D-optimal matrices and the designs achieving them are presented for the 4×5×m3, m3≥5 and 4×6×m3, m3≥6 saturated factorial designs in D.

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Cite

BibTeXRIS
BibTeX
@article{chatzopoulos2026doptimal,
  title = {{D-Optimal Saturated Factorial Designs with Three Factors}},
  author = {Stavros A. Chatzopoulos},
  journal = {Mathematics},
  year = {2026},
  month = nov,
  doi = {10.3390/math14213987},
  url = {https://www.mdpi.com/2227-7390/14/21/3987},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - D-Optimal Saturated Factorial Designs with Three Factors
AU  - Stavros A. Chatzopoulos
PY  - 2026
DA  - 2026/11/02
JO  - Mathematics
DO  - 10.3390/math14213987
UR  - https://www.mdpi.com/2227-7390/14/21/3987
AB  - The aim of this paper is to study the D-optimal m1×m2×m3, m3≥m2≥m1≥2 saturated factorial designs for estimating the mean and the main effects. A restricted class D of m1×m2×m3 saturated designs is defined. In this class, the upper bounds of the determinant values of D-optimal matrices for the already known 2×m2×m3, m3≥m2≥2, 3×m2×m2, m2≥3, 3×m2×(m2+1), m2≥3 and for 4×4×m3, m3≥4 saturated designs are found. New results regarding the determinant values of D-optimal matrices and the designs achieving them are presented for the 4×5×m3, m3≥5 and 4×6×m3, m3≥6 saturated factorial designs in D.
SN  - 2227-7390
ER  -