Orthogonal Arrays (Taguchi)

A full factorial of 3 factors at two levels will have everything at the high level.  For a fractional factorial (which is what you are describing) you may or may not depending on which half of the replicate you choose.
A  B   C  ABC
-1 -1 -1    -1
 1 -1 -1      1
-1  1 -1      1
 1  1 -1     -1
-1 -1  1      1
 1 -1  1     -1
-1  1  1     -1
 1  1  1       1
Choose the half fraction where ABC = 1 and your 4 experiments become
 1 -1 -1     
-1  1 -1      
-1 -1  1     
 1   1  1     
and you have all three at the high level but you don’t have all three at the low level.
  The other half fraction (with ABC = -1) gives you everyone at the low but not everyone at the high level.
-1 -1 -1    
 1  1 -1     
 1 -1  1     
-1  1  1    

Jack:When you have a sparsely populated orthogonal matrix, there are a number of different combinations of factor settings that satisfy your requirements of orthogonality. By coincidence, some may contain runs where all settings are low without a run where all settings are high. You may choose a different set (foldover) if you wish. This is true in an L4 design, but if it really bugs you, then go with an L8 design or higher.Cheers, BTDT

The real advantage of Orthogonal Arrays appears when the factors have more than three levels.
Jane

  While they are given different names in the Taguchi literature, orthogonal arrays are nothing more than factorial designs.  Almost any good book on experimental design should have a chapter devoted to their logic and construction.