Caps and Colouring Steiner Triple Systems

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 AG(5, 3) is 6-chromatic, and so we exhibit the first specific example of a 6-chromatic Steiner triple system.

• Type: Journal
• Year: 1998
• Where: DCC
• Authors: Aiden A. Bruen, Lucien Haddad, David L. Wehlau
• Keywords: Cardinality, Computer Graphics, DCC 1998, Largest Cap, Steiner Triple System