A study of hendecads

In this paper, we shall study the packings of v elements into hendecads for those values of v less than 111. The values k = 7 and k 11 are the first values for which a geometry does not exist, and the situation for k = 11 displays considerably more variety than that which' occurred for k = 7 (cf. [15]). First, we recapitulate terminology; we start with v elements, and wish to determine the packing number D(2,k,v) for v small. D(2,k,v) is the, cardinality of the largest family of k-sets chosen from the v elements in such a way that no pair occurs more than once. Saying that v is "small" means that v ~ k2 k + 1 (we shall thus be considering the case that k = 11, v ~ 111).