This program will generate matrices from a field of 8,9,10,11 and up to 21 numbers.  the program is complete, but it is very inefficient and extremely slow.....Need a better way!!!

It works by extracting natural groups of different field sets.  for example field  8 has 7 natural groups:

{4,8,12,16,20,24,28}

4............................produces a 4 by 6 matrix with each number occurring an equal amount of times: this group is 3

1-2-3-5-6-7

1-2-4-5-6-8

1-3-4-5-7-8

2-3-4-6-7-8

8...............................................Produces a 8 by 6 matrix with each number occurring  6 times

12.............................................Produces a 12 by 6 matrix with each number occurring 9 times

16.............................................Produces a 16 by 6 matrix with each number occurring 12 times

20.............................................Produces a 20 by 6 matrix with each number occurring 15 times

24.............................................Produces a 24 by 6 matrix with each number occurring 18 times

28.............................................Produces a 28 by 6 matrix with each number occurring 21 times

Now, these matrices are generated randomly because there are many different variations of each matrix.:

For example the 4 by 6 matrix from above has another variation:

 

1-2-4-5-6-7                     

1-2-3-5-6-7

1-2-4-5-6-8

2-3-4-6-7-8

And many more!...Can You Help?

 

 

 

 

1-2-3-5-6-7

1-2-4-5-6-8

1-3-4-5-7-8

2-3-4-6-7-8