Further Results on Quasi-Complete Latin Squares

Further results are given for quasi-complete latin squares. These are latin squares which have the property that every unordered pair of elements occurs next to each other exactly twice in rows and twice in columns. All possible squares with first row in natural order are considered up to size 6, while possible squares for sizes 7 to 9 are increasingly numerous so are considered progressively less exhaustively. Pairs of squares which together have equality of concurrences of ordered pairs of elements are also examined. The uses of quasi-complete squares for the practical design of field experiments requiring equality of occurrences of unordered pairs of neighbours are discussed.