Another approach...if you want 10 points in a 3D space, with no repeats of a coordinate in any dimension...

dim = 3;
numPts = 10;
Transpose@(Ordering /@ Ordering /@ RandomReal[1, {dim, numPts}])

$ \begin{array}{ccc} 8 & 6 & 4 \\ 7 & 5 & 8 \\ 2 & 4 & 1 \\ 5 & 8 & 5 \\ 9 & 3 & 2 \\ 10 & 7 & 9 \\ 1 & 2 & 10 \\ 4 & 1 & 7 \\ 6 & 9 & 6 \\ 3 & 10 & 3 \\ \end{array} $

Data sets in this form (each column is a permutation of Range[numPts]) have a bunch of interesting combinatorial properties. What is fascinating is to take the transform and apply it to random data that is distributed in unique ways, such as points on a simplex, hypersphere, etc.

Another approach...if you want 10 points in a 3D space, with no repeats of a coordinate in any dimension...

dim = 3;
numPts = 10;
Transpose@(Ordering /@ Ordering /@ RandomReal[1, {dim, numPts}])

$ \begin{array}{ccc} 8 & 6 & 4 \\ 7 & 5 & 8 \\ 2 & 4 & 1 \\ 5 & 8 & 5 \\ 9 & 3 & 2 \\ 10 & 7 & 9 \\ 1 & 2 & 10 \\ 4 & 1 & 7 \\ 6 & 9 & 6 \\ 3 & 10 & 3 \\ \end{array} $

Data sets in this form (each column is a permutation of Range[numPts]) have a bunch of interesting combinatorial properties. What is fascinating is to take the transform and apply it to random data that is distributed in unique ways, such as points on a simplex, hypersphere, etc.

Expanding a wee bit: the reason this transformation is interesting is that in algorithms to identify the Pareto frontier, you don't care about absolute values of a coordinate, just its ordinal value with respect to other values in a column. Once transformed, a bunch of shortcuts and interesting properties open up.

Another approach...if you want 10 points in a 3D space, with no repeats of a coordinate in any dimension...

dim = 3;
numPts = 10;
Transpose@(Ordering /@ Ordering /@ RandomReal[1, {dim, numPts}])

$ \begin{array}{ccc} 8 & 6 & 4 \\ 7 & 5 & 8 \\ 2 & 4 & 1 \\ 5 & 8 & 5 \\ 9 & 3 & 2 \\ 10 & 7 & 9 \\ 1 & 2 & 10 \\ 4 & 1 & 7 \\ 6 & 9 & 6 \\ 3 & 10 & 3 \\ \end{array} $

Data sets in this form (each column is a permutation of Range[numPts]) have a bunch of interesting combinatorial properties.

Another approach...if you want 10 points in a 3D space, with no repeats of a coordinate in any dimension...

dim = 3;
numPts = 10;
Transpose@(Ordering /@ Ordering /@ RandomReal[1, {dim, numPts}])

$ \begin{array}{ccc} 8 & 6 & 4 \\ 7 & 5 & 8 \\ 2 & 4 & 1 \\ 5 & 8 & 5 \\ 9 & 3 & 2 \\ 10 & 7 & 9 \\ 1 & 2 & 10 \\ 4 & 1 & 7 \\ 6 & 9 & 6 \\ 3 & 10 & 3 \\ \end{array} $

Data sets in this form (each column is a permutation of Range[numPts]) have a bunch of interesting combinatorial properties. What is fascinating is to take the transform and apply it to random data that is distributed in unique ways, such as points on a simplex, hypersphere, etc.