I think you might be looking for incomplete block designs. See Cochran and Cox 1957, page 481 for Plan 11.38 t=28, k=4, r=9, b=63, lambda=1, E=.78. Type I
This design might be the set of 4 x 7 matrices you are looking for. On Fri, Dec 12, 2014 at 12:00 PM, Kathryn Lord <kathryn.lord2...@gmail.com> wrote: > Dear all, > > Suppose that I have natural numbers 1 through 28. > > Based on these numbers, choose 4 numbers 7 times without replacement and > make a 4 by 7 matrix, for example, > >> a1 > [,1] [,2] [,3] [,4] [,5] [,6] [,7] > [1,] 1 5 9 13 17 21 25 > [2,] 2 6 10 14 18 22 26 > [3,] 3 7 11 15 19 23 27 > [4,] 4 8 12 16 20 24 28 > > and again create another 4 * 7 matrix, say a2, in the same way; however, > every element of each column in a2 does not exist in any column of a1 like > this, e.g. > >> a2 > [,1] [,2] [,3] [,4] [,5] [,6] [,7] > [1,] 1 2 3 4 5 6 7 > [2,] 8 9 10 11 12 13 14 > [3,] 15 16 17 18 19 20 21 > [4,] 22 23 24 25 26 27 28 >> > > and again create another 4 * 7 matrix, say a3, in the same way; however, > every element of each column in a3 does not exist in any column of a1 and > a2. > > Using same logic, I'd like to make the matrices (a3, a4, a5....) as many as > possible. > > > Any suggestion will be greatly appreciated. > > Best, > > Kathryn Lord > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
