(22, 33, 12, 8, 4)-BIBD, an Update
A (v, b,r, k, λ)-balanced incomplete block design is a family of b sets (called blocks) of size k whose elements (varieties) are from a v-set, v > k, such that every element occurs exactly r times and every pair exactly λ times. A (22, 33, 12, 8, 4)-BIBD is the set of parameters with the smallest v for which it is not known whether a BIBD exists or not. A survey of what is known about such a design is given.
KeywordsAutomorphism Group Element Orbit Incidence Matrix Dual Code Steiner Triple System
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- C. Demeng, M. Greig, and G.H.J. van Rees. non-existent preprint.Google Scholar
- R.A. Fisher and F. Yates. Statistical Tables for Biological, Agricultural and Medical Research, volume 93. Hafner, New York, 6th edition edition, 1963.Google Scholar
- M. Greig. An improvement to connor’s criterion. preprint.Google Scholar
- M. Hall Jr. Constructive methods for designs. Cong. Numer., 66 (1988), 141–144.Google Scholar
- S. Kapralov. Combinatorial 2-(22,8,4) designs with automorphisms of order 3 fixing one point. In Math. and Education in Math., Proc. of the XVI Spring Conference of Union of Bulgarian Mathematicians, pages 453–458. Sunny Beach, 1987.Google Scholar
- B.D. McKay and S.P. Radziszowski. Towards deciding the existence of 2-(22,8,4) designs. J. Comb. Math. Comb. Comp.. submitted.Google Scholar