Lucien Haddad

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Hill [6] showed that the largest cap in PG(5, 3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 in AG(5, 3). Here we show that the size of a cap in AG(5, 3) is bounded above by 48. We also give an example of three disjoint 45-caps in AG(5, 3). Using these two results we are able to prove that the Steiner triple system(More)
A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactly one triple of B. It is well known that a necessary and sufficient condition for a STS(v) to exist is that v#1 or 3 (mod 6). An r-coloring of a STS(v) is a map ,(More)