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On the maximum sizes of certain (k, n)-arcs in finite projective geometries

Published online by Cambridge University Press:  24 October 2008

J. R. M. Mason
Affiliation:
G.E.C. Hirst Research Centre, Wembley

Extract

In this paper the values of m(6)2,9, m(5)2,8 and m(5)2,9 have been determined as well as improved bounds on other arcs, and in particular a general construction for certain large arcs in planes of square order has been given. Table 5 summarizes the known values of m(n)2, q for 2 ≤ nq and q ≤ 9.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Barlotti, A.Sui {k; n}-archi di un piano lineare finito. Bull. Un. Mat. Ital. 11 (1956), 553556.Google Scholar
(2)Barlotti, A.Some topics in finite geometrical structures (Institute of Statistics, mimeo series, no. 439, University of North Carolina, 1965).Google Scholar
(3)Barnabei, M., Searby, D. and Zucchini, C.On small {k; q}-arcs in planes of order q 2. J. Combin. Theory Ser. A, 24 (1978), 241246.CrossRefGoogle Scholar
(4)Bose, R. C.Mathematical theory of the symmetrical factorial design. Sankyā 8 (1947), 107166.Google Scholar
(5)Bose, R. C.On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements (Golden Jubilee Commemoration Volume, Calcutta Math. Soc, 1958–9), 341354.Google Scholar
(6)Bramwell, D. L. Ph.D. Thesis, University of London, 1973.Google Scholar
(7)Ciechanowicz, Z. Ph.D. Thesis, University of London, 1980.Google Scholar
(8)Cossu, A.Su alcune proprietà dei (k; n)-archi di un piano proiettivo sopra un corpo finito. Rend. Mat. e Appl. 20 (1961), 271277.Google Scholar
(9)Denniston, R. H. F.Some maximal arcs in finite projective planes. J. Combin. Theory, Ser. A, 6 (1969), 317319.CrossRefGoogle Scholar
(10)Hill, R. and Mason, J. R. M. On (k, n)-arcs and the falsity of the Lunelli-Sce conjecture. Finite Geometries and Designs, Lond. Math. Soc. Lecture Notes Ser. 49 (University Press, Cambridge, 1980), pp. 153168.Google Scholar
(11)Hirschfeld, J. W. P.Projective geometries over finite fields (Clarendon Press, Oxford, 1979).Google Scholar
(12)Lunelli, L. and Sce, M.Considerazioni arithmetiche e risultati sperimentali sui {K; n}, q archi. Ist. Lombardo Accad. Sci. Rend. A 98 (1964), 352.Google Scholar
(13)Mason, J. R. M. Ph.D. Thesis, University of Salford, 1980.Google Scholar
(14)Thas, J. A.Some results concerning {(q+1)(n–1); n}-arcs and {(q+1) (n–1)+1; n}-arcs in finite projective planes of order q. J. Combin. Theory Ser. A 19 (1975), 228232.CrossRefGoogle Scholar