🚀 go-pugleaf

|> Suppose you have N groups of cells.  Each group contains K cells.
|> Now suppose you make choices consisting of one cell chosen from
|> each of the N groups.  Let each such choice be called a vector.
|> Clearly there are K^N unique vectors.
|> 
|> My question is:  what is the largest set of vectors you can pick
|> such that no two of the vectors overlap (i.e. have the same cell)
|> at more than Q of the groups (where Q < N)?

In more usual language, you want your vectors to differ in at least N-Q places. I
shall call this number D.

You are looking for the largest code with minimum distance D among your K^N
vectors.

Each vector has       (N+D)   neighbours  at diostance less than D, so a 
		      ( D )
		(K-1)^

simple upper bound on the size of your code is  

			  -(N+D/2)	
		K^N (K-1)^ ( D/2 )

(that's K to the N times (K-1) to the N+D/2 choose D/2).

Anyway, you want to look at Codes, Groups and Sphere Packings by J.H.Conway and
N.J.A. Sloane.

		Steve Linton