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All the Fibonacci groups in the family F(2, n) have been either fully identified or determined to be infinite, bar one, namely F(2, 9). Using computer-aided techniques it is shown that F(2, 9) has a quotient of order 152.5741, and an explicit matrix representation for a quotient of order 152.518 is given. This strongly suggests that F(2, 9) is infinite, but no proof of such a claim is available.
A method of construction of designs with parameters v1 = r2 = p2, r1 = v2 = p + 1, b = p(p+1), k = p which may be used for the two-way elimination of heterogeneity is discussed. These designs were first studied in connection with estimating tobacco mosaic virus. Our designs have the advantage that every treatment occurs at most once in a row or column. We give the designs explicitly for p = 3, 4, 5.
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