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What does the image under the action of matrix mean?
as follows

Balanced block design is an extension of traditional balanced incomplete block design (BIBD), partially balanced incomplete block design (PBIBD) and Latin matrix (or Latin square) design. This block design is weaker than the traditional block design, and there are more balanced block designs that meet the new equilibrium conditions, which are easier to construct. The newly constructed block design still maintains the original various forms of block design.