# zbMATH — the first resource for mathematics

Pooling, lattice square, and union jack designs. (English) Zbl 0938.05006
A union jack design of order $$n$$ is a collection of $$n \times n$$ arrays with distinct entries from a set $$X$$ of $$n^2$$ points such that every pair of points appears exactly once among the rows, columns, front diagonals, and back diagonals of the arrays. The authors show that union jack designs of order $$n$$ exist whenever $$n$$ is prime and $$n \equiv 3\pmod 4$$.

##### MSC:
 05B05 Combinatorial aspects of block designs
##### Keywords:
pooling design; affine plane; group testing; union jack design
Full Text:
##### References:
 [1] D.J. Balding, W.J. Bruno, E. Knill, and D.C. Torney, A comparative survey of nonadaptive pooling designs, In: Genomic Mapping and DNA Sequencing, IMA, Vol. 81, 1996, pp. 133–154. · Zbl 0860.62083 [2] T. Beth, D. Jungnickel, and H. Lenz, Design Theory, Cambridge University Press, Cambridge, 1986. [3] W.G. Cochran and G.M. Cox, Experimental Designs, John Wiley & Sons, Inc., New York, 1950, pp. 346–369. [4] C.J. Colbourn and J.H. Dinitz, Eds., The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, 1996. · Zbl 0836.00010 [5] W.T. Federer, Experimental Design, Macmillan & Co., New York, 1955, pp. 378–388. [6] W.T. Federer and J. Wright, Construction of lattice square designs, Biom. J.1 (1988) 77–85. · Zbl 0709.62068 · doi:10.1002/bimj.4710300114 [7] M. Kallaher, Translation planes, In: Handbook of Incidence Geometry, F. Buekenhout, ed., Elsevier North-Holland, 1995, pp. 137–192. · Zbl 0831.51004 [8] E. Knill, D.J. Balding, and D.C. Torney, Interpretation of pooling experiments using the Markov chain Monte Carlo method, J. Comput. Biol.3 (1996) 395–406. · doi:10.1089/cmb.1996.3.395 [9] K. Longmire et al., Semi-automated high precision pooling of large genomic libraries using the Robbins hydra, Biotechniques, in preparation. [10] J.K. Percus, D.E. Percus, W.J. Bruno, and D.C. Torney, Asymptotics of pooling design performance, J. Applied Prob., to appear. · Zbl 0967.62057 [11] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, John Wiley & Sons, New York, 1971. · Zbl 0222.62036 [12] F. Yates, A further note on the arrangement of variety trials: quasi-Latin squares, Ann. Eugenics7 (1937) 319–331. · JFM 63.1129.13 · doi:10.1111/j.1469-1809.1937.tb02150.x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.