How can I generate a randomized vector of repeating numbers with given conditions?

I'm trying to generate a vector of pseudo-random numbers that contains 1:11 repeated 8 times. The vector is broken up into blocks of 8. No number within each block can be repeated and each number has to occur at each position within the block once (i.e the number 4 has to occur first-eighth in eight different blocks). I've gone through a ton of iterations to do this and have attached the most recent attempt. The problem here is that by the end of the loop, the only possible numbers remaining are ones that have already been added within the current block of 8 numbers, so it becomes an endless while loop. Any help would be much appreciated!

TargTest=nan(8,11);%M by N array to indicate if Nth target was tested at Mth location
  TestSessionTargs=[]; %Test Session Target order
  while length(TestSessionTargs)<numel(TargTest)
      TestBlock=nan(1,8);
      for B=1:length(TestBlock)
          PossibleTargs=find(isnan(TargTest(B,:))==1);
          if length(PossibleTargs)~=1
              F=randsample(PossibleTargs,1);
              while ismember(F,TestBlock)
                  F=randsample(PossibleTargs,1);
              end
          else
              F=PossibleTargs;
          end
          TestBlock(B)=F
          TargTest(B,F)=1;
      end
      TestSessionTargs=[TestSessionTargs TestBlock];
  end

[Walter Roberson]

Are the blocks "sliding" blocks? Could a 7 from one block happen to be at the end of the block, and a 7 happen to be at the beginning of the next block?

[Karthik]

Below is a check that I use on the vector to tell me if that number has been tested at the position in the block and the block number it is located in

y2=reshape(TestSessionTargs,8,11);
  TestedVal=nan(size(y2)); %Each column represents target location. Each row represents Nth trial in Test block
  TestedValLoc=cell(size(y2));
  for M=1:size(y2,1)
      for N=1:size(y2,2)
          if isnan(TestedVal(M,y2(M,N)))
              TestedVal(M,y2(M,N))=1;
              TestedValLoc{M,y2(M,N)}=[TestedValLoc{M,y2(M,N)} N];
          else
              TestedVal(M,y2(M,N))=TestedVal(M,y2(M,N))+1; %Tells us how many times location was tested
              TestedValLoc{M,y2(M,N)}=[TestedValLoc{M,y2(M,N)} N]; %Tells us block this location was tested in
          end
      end
  end

[Walter Roberson]

If you have blocks of 8, but you have 11 different values 1:11, then how can each of the 11 different values occur once in each position?

Or is the idea that a pseudo-random subset of 8 of the 11 will be chosen, and after that the conditions must be filled for that subset?

[Karthik]

Yes, that can happen

[1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1] is an example of two consecutive valid blocks where 8 values occur at different positions within the blocks but do not repeat within the same block.

[Karthik]

I have 11 different values repeated 8 times, so that's 88 values broken up into blocks of 8. The 88 values need to be arranged in the way that I mentioned

[Karthik]

Another attempt I have made:

TargTest=nan(8,11);%M by N array to indicate if Nth target was tested at Mth location
TestSessionTargs=[]; %Test Session Target order

%While loop will go through TargTest M*N times row-wise and choose random 
%index that ~isnan once it chooses that index in TargTest, places 1 as
%place holder to say location has been tested at particular time.
while length(TestSessionTargs)<numel(TargTest)
    TestBlock=nan(1,8);
    for B=1:size(TargTest,1)
        F=randi(11,1);
        while ~isnan(TargTest(B,F))||ismember(F,TestBlock)
            F=randi(11,1);
        end
        TestBlock(B)=F;
        TargTest(B,F)=1;
    end

      TestSessionTargs=[TestSessionTargs TestBlock];
  end

[ali mokhtar]

targtest=ntest(13:end);

what do you mean

Answer 1

[Walter Roberson]

If each symbol in the current symbol set must occur exactly once in each position over the block of 8, then you should research Latin Squares of Order 8. See here

[Karthik]

Thanks, so because I'm essentially doing an 8 by 11, because it's not square it's going to be impossible?

[Karthik]

Ah I looked at the latin square. the problem here is that from what I see, everything is in order. Another stipulation is that we do want to keep randomization, so rather than saying [1 2 3 4 5 6 7 8], it should be something more random like [7 2 3 6 1 5 8 4]

[Karthik]

This works! There's a file exchange for a latin square function latsq that also provides randomized latin squares to solve the problem.

Thank you for the direction!