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Martin Grüttmüller     Ian T. Roberts     Sue D’Arcy     Judith Egan

The minimum number of blocks in Pairwise Balanced Designs with maximum block size 4 : the final cases

University of Rostock, Institute of Mathematics, 2005

https://doi.org/10.18453/rosdok_id00005834

Abstract: The minimum number of blocks having maximum size precisely four that are required to cover, exactly λ times, all pairs of elements from a set of cardinality v is denoted by gλ(4)(v) are known except for λ = 1 andv = 17 or 18. It is known that 30<= g(4)(17) <= 31 and 32 <= g(4)(18) <= 33. In this paper we Show that g(4)(17) =/ 30 and g(4)(18) =/ 32, thus finalising the Determination of gλ(4)(v) for all λ and v

working paper   free access