Geodesic
The Spectra for the Conjugate Invariant Subgroups of n 2 × 4 Orthogonal Arrays
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1126-1139

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An n 2 × k orthogonal array is a pair (P, B) where P = {1, 2, ..., n} and B is a collection of k-tuples of elements from P (called rows) such that if i < j ∈ {1, 2, ..., k} and x and y are any two elements of P (not necessarily distinct) there is exactly one row in B whose ith coordinate is x and whose jth coordinate is y. We will refer to the ith coordinate of a row r as the ith column of r. The number n is called the order (or size) of the array and k is called the strength. 
Lindner, C. C.; Mullin, R. C.; Hoffman, D. G. The Spectra for the Conjugate Invariant Subgroups of n 2 × 4 Orthogonal Arrays. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1126-1139. doi: 10.4153/CJM-1980-086-9
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[1] 1. Bermond, J. C., Germa, A., and Sotteau, D., Resolvable decompositions of K*, J. Combinational Theory, Ser. A 26 (1979), 179–185. Google Scholar

[2] 2. Bose, R. S., Shrikhande, S. S., and Parker, E. T., Further results on the construction of mutually orthogonal latin squares and the falsity of Ruler's conjecture, Can. J. Math. 12 (1960), 189–203. Google Scholar

[3] 3. Brayton, R. K., Coppersmith, D., and Hoffman, A. J., Self-orthogonal latin squares of all orders n ≠ 2, 3, 6, Bull. Amer. Math. Soc. 80 (1974), 116–118. Google Scholar

[4] 4. Hanani, H., The existence and construction of balanced incomplete block designs, Ann. Math. Stat. 32 (1961), 361–386. Google Scholar

[5] 5. Hanani, H., On balanced incomplete block designs with blocks having five elements, J. Combinatorial Theory 12 (1972), 184–201. Google Scholar

[6] 6. Lindner, C. C., On the construction of cyclic quasigroups, Discrete Math. 6 (1973), 149–158. Google Scholar

[7] 7. Lindner, C. C. and Steedley, D., On the number of conjugates of a quasigroup, Algebra Universalis 5 (1975), 191–196. Google Scholar

[8] 8. Lindner, C. C. and Mendelsohn, E., On the conjugates on an n2 × 4 orthogonal array, Discrete Math. 20 (1977), 123–132. Google Scholar

[9] 9. Lindner, C. C., Mendelsohn, N. S., and Sun, S. R., On the construction of Schroeder quasigroups, Discrete Math, (to appear). Google Scholar | DOI

[10] 10. Mendelsohn, N. S., Combinatorial designs as models of universal algebras, Recent Progress in Combinatorics (Academic Press Inc., New York, 1969). Google Scholar

[11] 11. Mendelsohn, N. S., Mendelsohn, E. and Bennett, F. E., Resolvable perfect cyclic designs, J. Combinatorial Theory, Ser. A 29 (1980), 142–150. Google Scholar

[12] 12. Schelienberg, P. J., Vanstone, S. A., and van Reese, G. H. J., Fourppairwise orthogonal latin squares of side 15, Ars Combinatoria 6 (1978), 141–150. Google Scholar

[13] 13. Wilson, R. M. and Wang, S. M. P., A few more squares, II, Proc. 9th Southeastern Conf. Combinatorics, Graph Theory, and Computing (Boca Raton, 1978), (to appear). Google Scholar

[14] 14. Wilson, R. M., An existence theory for pairwise balanced designs, I. Composition theorems and morphism, J. Combinatorial Theory 13 (1972), 220–245. Google Scholar

[15] 15. Wilson, R. M., Constructions and uses of pairwise balanced designs, Proc. Advanced Study Inst, on Combinatorics, Breukelen (1974), 18–41, Math. Centre Tracts 55, Math. Centrum, Amsterdam (1974). Google Scholar

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