Define the degree of a design to be the number of values taken by the cardinality of |x ⋂ y|, as x and y range over the distinct blocks of the design. Then Ray-Chaudhuri and Wilson proved in 1975 that

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a t-design with v points contains at least ( v ⌊ t / 2 ⌋ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137131/3e789cab-79f2-434a-a841-e2acf5146c2d/content/eq1338.tif"/> distinct blocks.