Geodesic
The Spectrum of Orthogonal Steiner Triple Systems
Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 239-252

Voir la notice de l'article provenant de la source Cambridge University Press

Two Steiner triple systems (V, B) and (V, D) are orthogonal if they have no triples in common, and if for every two distinct intersecting triples {x,y,z} and {x, y, z} of B, the two triples {x,y,a} and {u, v, b} in (D satisfy a ≠ b. It is shown here that if v ≡ 1,3 (mod 6), v ≥ 7 and v ≠ 9, a pair of orthogonal Steiner triple systems of order v exist. This settles completely the question of their existence posed by O'Shaughnessy in 1968.
DOI : 10.4153/CJM-1994-010-7
Mots-clés : 05B07 
Colbourn, Charles J.; Gibbons, Peter B.; Mathon, Rudolf; Mullin, Ronald C.; Rosa, Alexander. The Spectrum of Orthogonal Steiner Triple Systems. Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 239-252. doi: 10.4153/CJM-1994-010-7
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