Abstract
We construct two pure partial planes of order 6 with 25 lines, which extend the dual of the linear space PG(3,2). One of these is of particular interest since its dual is a pseudo-complement of a triangle in a projective plane of order 6.
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Batten L.M., Beutelspacher A.: The Theory of Finite Linear Spaces. Cambridge University Press, Cambridge (1993)
Bruck R.H., Ryser H.J.: The nonexistence of certain finite projective planes. Canad. J. Math. 1, 88–93 (1949)
Colbourn C.J., Dinitz J.H.: CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton (1996)
Euler L.: Recherches sur une nouvelle espèce des quarrés magiques. Verh Zeeuwsch Genootsch Wetensch Vlissingen 9, 85–239 (1782)
Hering C., Krebs A.: A partial plane of order 6 constructed from the icosahedron. Des. Codes Cryptogr. 44, 287–292 (2007)
Hirschfeld J.W.P.: Finite Projective Spaces of Three Dimensions. Oxford University Press, Oxford (1985)
McCarthy R.C., Mullin R.C., Schellenberg P.J., Stanton R.G., Vanstone S.A.: On approximations to a projective plane of order 6. Ars Comb. 2, 111–168 (1976)
Ralston T.: On the embeddability of the complement of a complete triangle in a finite projective plane. Ars Comb. 11, 271–274 (1981)
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Communicated by J. W. P. Hirschfeld.
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Prince, A.R. Pure partial planes of order 6 with 25 lines. Des. Codes Cryptogr. 52, 243–247 (2009). https://doi.org/10.1007/s10623-009-9279-x
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DOI: https://doi.org/10.1007/s10623-009-9279-x