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%I #17 May 06 2020 01:33:42
%S 4,5,6,9,11,13,16
%N Block sizes k of nontrivial biplanes.
%C A biplane is an incidence structure consisting of a set P of h points and a set of h blocks, each of which is an k-subset of P (block size k), such that every pair of points lies in exactly 2 blocks (see Alavi et al.).
%H Seyed Hassan Alavi, Ashraf Daneshkhah, Cheryl E Praeger, <a href="https://arxiv.org/abs/2004.04535">Symmetries of biplanes</a>, arXiv:2004.04535 [math.GR], 2020. See Introduction p. 1.
%H P. Kaski and P. R. J. Östergård. <a href="https://doi.org/10.1002/jcd.20145">There are exactly five biplanes with k = 11</a>, J. Combin. Des., 16(2):117-127, 2008.
%Y Cf. A001109, A003409, A038723, A038725, A054490, A334456 (h).
%K nonn,more
%O 1,1
%A _Stefano Spezia_, Apr 30 2020