Geodesic
Block Sizes in Pairwise Balanced Designs
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 375-380

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The number of sets of integers which are realizable as block sizes of a pairwise balanced design of order n is between and ; in contrast, when the multiplicity of each block size is also specified, the number of multisets which can be realized is between and . Although this gives a reasonable bound on the number of multisets which can be realized, a good characterization is not likely to exist; deciding whether a multiset can be so realized is NP-complete.
DOI : 10.4153/CMB-1984-057-0
Mots-clés : 05B30, 05B05 
Colbourn, Charles J.; Phelps, Kevin T.; Rödl, Vojtěch. Block Sizes in Pairwise Balanced Designs. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 375-380. doi: 10.4153/CMB-1984-057-0
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