Graeco-Latin cubes

Vladimir Potapov
A Latin square of order q is a q×q array with elements from {0,1,...,q-1} such that each value occurs exactly once in each row and column. Two Latin squares G and L are orthogonal if (G(x,y), L(x,y)) = (u,v) has exactly one solution for each (u,v) from {0,1,...,q-1}×{0,1,...,q-1}. The square obtained by superimposing two orthogonal Latin squares to get entries with pairs of elements is called a Graeco-Latin square. A Latin cube of order q...
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