Maximal caps in AG (6, 3)

We show that there are no complete 44-caps in AG(5, 3). We then use this result to prove that the maximal size for a cap in AG(6, 3) is equal to 112, and that the 112-caps in AG(6, 3) are unique up to affine equivalence.      

Partitioning Quadrics, Symmetric Group Divisible Designs and Caps

Using partitionings of quadrics we give a geometric construction of certain symmetric group divisible designs. It is shown that some of them at least are self-dual. The designs that we construct here relate to interesting work — some of it very recent — by D. Jungnickel and by E. Moorhouse. In this paper we also give a short proof of an old result of G. Pellegrino concerning the maximum size of a cap in AG(4,3) and its structure. Semi-biplanes make their appearance as part of our construction in the three dimensional case.     

Veronese Varieties Over Finite Fields and Their Projections

Inthis paper Veronese varieties of degree d over aGalois field are studied. We also show that some of known capsembedded into classical varieties always are projections of Veronesevarieties.     

Classification and Constructions of Complete Caps in Binary Spaces

We give new recursive constructions of complete caps in PG(n,2). We approach the problem of constructing caps with low dependency via the doubling construction and comparison to lower bounds. We report results of the exhaustive classification (up to projective equivalence) of all caps in PG(n,2) for n≤ 6. Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)     

Large Caps in Small Spaces

We construct large caps in projective spaces of small dimension (up to 11) defined over fields of orderat most 9. The constructions are both theoretical and computer-supported. Some more computer-generated 4-dimensional caps over larger fields are alsomentioned.