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A latin rectangle is an m × n array, m ≤ n, from the numbers 1, 2,. .. , n such that each of these numbers occur in each row and in each column at most once. A critical set in an m×n array is a set S of given entries, such that there exists a unique extension of S to a latin rectangle of size m×n. If we index the rows and columns of an m×n array, m ≤ n, by(More)
In a 4-(12, 6, 4) design a block is either disjoint from one other block or it has five points in common with one other block. For a 4-(12, 6, 4) design with a pair of blocks of the second type it is shown that· another thirty blocks of the design can be completed in a unique way and these thirty blocks contain a copy of a 3-(10, 4, 1) design.
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