## Introduction

A (non-resolvable) row-column design (RCD) is an arrangement of *v*
treatments set out in *kxb* array such that each treatment is replicated
*r* times (*vr=kb*). We say this RCD is of size (*v,k,b*). A
recommended reference on the subject is Chapter 5 of John & Williams
(1995).

RCD is a Gendex program for constructing optimal or near-optimal row-column designs. The approach adopted by RCD is to permute the treatments within the blocks of an optimal or near-optimal block design used as the column component of the RCD. The optimality criterion and the algorithm used in RCD are discussed in Nguyen (1997).

## Using RCD

Let's assume all Gendex class files are in the directory c:\gendex and
suppose you want to construct an RCD of size (*v,k,b*)=(9,3,6). The
following is the file bib.txt in the working directory
which contains an IBD of size (*v,k,r*)=(9,3,2) with blocks as columns:

5 6 3 4 8 5 0 7 7 8 1 1 4 0 2 3 6 2

At the working directory, type the following command at the Command Prompt (case is important):

java -cp c:\gendex RCD

The RCD GUI will pop up. Enter *bib.txt* in the **File** text
field:

Click **START**, RCD will start running and after try 10, the plan of
the constructed design for this try pops up in the RCD output window
(as the ratio *E/U* reaches 1) and RCD stops:

The **START** button has changed to **RESET** button. If you
click this **RESET** button, the output will disappear and you can
now start a new design problem. Note that the default random seed is the
one obtained from the system clock and the default number of tries is 1000. You
can change these default values if you wish to.

## Output

The result of the best try is displayed in the RCD output
window and is also saved in the file RCD.htm in the working directory. This
file can be read by a browser such as IE or *Google Chrome*. Information for
this try includes:

- Try number;
- The number of iterations;
- The objective function
*f*. - The row, column and row-column efficiency
*E*of the constructed design and the ratio*E/U*where*U*is the upper bound of an RCD of size (*v,k,b*). The program automatically stops if this ratio reaches 1. - The distribution of the concurrences of this design;
- The design plan and the associated random seed;
- The time in seconds RCD used to construct the above design.

An additional output of an RCD session is the file form.htm. This file contains the randomized plan of the constructed design.

## Examples

- An RCD of size (
*v,k,b*)=(4,6,6) (http://designcomputing.net/gendex/rcd/r1.html). - An RCD of size (
*v,k,b*)=(10,5,6) (http://designcomputing.net/gendex/rcd/r2.html). - An RCD of size (
*v,k,b*)=(8,4,4) (http://designcomputing.net/gendex/rcd/r3.html). - An RCD of size (
*v,k,b*)=(9,3,6) (http://designcomputing.net/gendex/rcd/r4.html). - An RCD of size (
*v,k,b*)=(12,4,6) (http://designcomputing.net/gendex/rcd/r5.html). - An RCD of size (
*v,k,b*)=(12,4,9) (http://designcomputing.net/gendex/rcd/r6.html). - An RCD of size (
*v,k,b*)=(16,4,12) (http://designcomputing.net/gendex/rcd/r7.html). - An RCD of size (
*v,k,b*)=(6,4,9) (http://designcomputing.net/gendex/rcd/r8.html). - An RCD of size (
*v,k,b*)=(9,6,6) (http://designcomputing.net/gendex/rcd/r9.html). - An RCD of size (
*v,k,b*)=(15,6,10) (http://designcomputing.net/gendex/rcd/r10.html).

**Notes**:

## References

John, J.A. & Williams E.R. (1987) *Cyclic designs and
computer-generated designs*. New York: Chapman & Hall.

Nguyen, N-K (1997) Construction of optimal row-column designs by computer.
*Computing Science & Statistics* **28**, 471-475.

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