No extendable biplane of order nine

Bagchi, Bhaskar (1988) No extendable biplane of order nine Journal of Combinatorial Theory, Series A, 49 (1). pp. 1-12. ISSN 0097-3165

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We prove the nonexistence of 3 - (57, 12, 2) designs. This is achieved by a detailed analysis of the ternary code of a putative 3-design with these parameters. In view of a theorem of Mesner, our result is equivalent to nonexistence of triangle-free strongly regular graphs of order 324 and valency 57.

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