On small 3-nets embedded in a projective plane over a field

Nagy, Gábor Péter and N, Pace (2013) On small 3-nets embedded in a projective plane over a field. JOURNAL OF COMBINATORIAL THEORY SERIES A, 120 (7). pp. 1632-1641. ISSN 0097-3165

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Abstract

In this paper, we investigate dual 3-nets realizing the groups C3 × C3, C2 × C4, Alt4 and that can be embedded in a projective plane P G(2, K), where K is an algebraically closed field. We give a symbol- ically verifiable computational proof that every dual 3-net realizing the groups C3 × C3 and C2 × C4 is algebraic, namely, that its points lie on a plane cubic. Moreover, we present two computer programs whose calculations show that the group Alt4 cannot be realized if the characteristic of K is zero.

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