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chemical balance weighing design; ternary balanced block design

References:

[1] Banerjee K. S.: **Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics**. Marcel Dekker, New York 1975 MR 0458751 | Zbl 0334.62030

[2] Billington E. J.: **Balanced $n$-array designs: a combinatorial survey and some new results**. Ars Combin. 17A (1984), 37–72 MR 0746174

[3] Billington E. J., Robinson P. J.: **A list of balanced ternary block designs with $r \le 15$ and some necessary existence conditions**. Ars Combin. 16 (1983), 235–258 MR 0734059

[4] Ceranka B., Graczyk M.: **Optimum chemical balance weighing designs under the restriction on weighings**. Discuss. Math. 21 (2001), 111–120 DOI 10.7151/dmps.1024 | MR 1961022

[5] Ceranka B., Katulska K.: **On some optimum chemical balance weighing designs for $v+1$ objects**. J. Japan Statist. Soc. 18 (1988), 47–50 MR 0959679 | Zbl 0651.62072

[6] Ceranka B., Katulska K.: **Chemical balance weighing designs under the restriction on the number of objects placed on the pans**. Tatra Mt. Math. Publ. 17 (1999), 141–148 MR 1737701 | Zbl 0988.62047

[7] Ceranka B., Katulska, K., Mizera D.: **The application of ternary balanced block designs to chemical balance weighing designs**. Discuss. Math. 18 (1998), 179–185 MR 1687875

[8] Hotelling H.: **Some improvements in weighing and other experimental techniques**. Ann. Math. Statist. 15 (1944), 297–305 DOI 10.1214/aoms/1177731236 | MR 0010951 | Zbl 0063.02076

[9] Raghavarao D.: **Constructions and Combinatorial Problems in Designs of Experiments**. Wiley, New York 1971 MR 0365935

[10] Saha G. M., Kageyama S.: **Balanced arrays and weighing designs**. Austral. J. Statist. 26 (1984), 119–124 DOI 10.1111/j.1467-842X.1984.tb01225.x | MR 0766612 | Zbl 0599.62089

[11] Shah K. R., Sinha B. L.: **Theory of Optimal Designs**. Springer, Berlin 1989 MR 1016151 | Zbl 0688.62043

[12] Swamy M. N.: **Use of balanced bipartite weighing designs as chemical balance designs**. Comm. Statist. Theory Methods 11 (1982), 769–785 DOI 10.1080/03610928208828270 | MR 0651611 | Zbl 0514.62086