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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
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