Latin squares and related experimental designs
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چکیده
A Latin square is an arrangement of v copies of v symbols into a v× v square so that (i) each symbol occurs once in each row, and (ii) each symbol occurs once in each column. Three distinct Latin squares of order v = 4 are shown in Example 1. Other than for small v, the number of distinct (non-identical as matrices) Latin squares is not generally known, though it is known that it grows rapidly with v. For v = 3 the number of distinct Latin squares is 12, for v = 7 is greater than 6.1× 10, and for v = 11 is greater than 7.7× 10; see Laywine and Mullen (1998, chapter 1).
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