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The connection between maximal caps (sometimes called complete caps) and certain binary codes called quasi-perfect codes is described. We provide a geometric approach to the foundational work of Davydov and Tombak who have obtained the exact possible sizes of large maximal caps. A new self-contained proof of the existence and the structure of the largest… (More)
Hill  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 coloring of a Steiner triple system is equitable if the cardinalities of the color classes differ by at most one. It is shown that, with the possible exceptions of, there exists for all v#1, 3 (mod 6) and v15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. 1997 Academic Press
We show that, up to an automorphism, there is a unique independent set in PG(5,2) that meet every hyperplane in 4 points or more. Using this result, we show that PG(5,2) is a 5-chromatic STS. Moreover, we construct a 5-chromatic STS(v) for every admissible v ≥ 127.