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Caps and Colouring Steiner Triple Systems   
摘  要:   Hill (6) showed that the largest cap inPG.5; 3/ has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 inAG.5; 3/. Here we show that the size of a cap inAG.5; 3/ is bounded above by 48. We also give an example of three disjoint 45-caps inAG.5; 3/. Using these two results we are able to prove that the Steiner triple systemAG.5; 3/ is 6-chromatic, and so we exhibit the first specific example of a 6-chromatic Steiner triple system.
发  表:   Designs, Codes and Cryptography  1998

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