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- W125989737 abstract "This paper shows that any Latin square of side u can be a subsquare of the multiplication table of a Steiner triple system of size 3u + k, where k depends only on the residue class of u modulo 6, and of Steiner triple systems all of sizes at least 6u + 2k + 1. A generalization of “conjugate” to subsquares is given and it is then shown that if a Latin square is a subsquare of Steiner quasigroup then so are all its subsquare conjugates. Finally, as an application it is shown that if a square is part of a family of s + 1 mutually orthogonal Latin squares of side u then a Generalized Howell Design (s, 3, u, 3u) exists which is embeddable in a Steiner quasigroup of size 3u +k." @default.
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- W125989737 date "1984-01-01" @default.
- W125989737 modified "2023-09-26" @default.
- W125989737 title "Embedding Latin Squares in Steiner Quasigroups, and Howell Designs in Triple Systems" @default.
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- W125989737 doi "https://doi.org/10.1016/s0304-0208(08)72806-8" @default.
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