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# Blocking semiovals of Type (1,M+1,N+1)

Batten, Lynn and Dover, Jeremy 2001, Blocking semiovals of Type (1,M+1,N+1), SIAM journal of discrete mathematics, vol. 14, no. 4, pp. 446-457.

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Title Blocking semiovals of Type (1,M+1,N+1) Batten, Lynn Dover, Jeremy SIAM journal of discrete mathematics 14 4 446 457 Society for Industrial & Applied Mathematics Philadelphia, Pa. 2001 0895-4801 projective planes blocking sets semiovals We consider the existence of blocking semiovals in finite projective planes which have intersection sizes 1, m+1 or n+1 with the lines of the plane for $1 \leq m < n$. For those prime powers $q \leq 1024$, in almost all cases, we are able to show that, apart from a trivial example, no such blocking semioval exists in a projective plane of order q. We are also able to prove, for general q, that if q2+q+1 is a prime or three times a prime, then only the same trivial example can exist in a projective plane of order q. eng 010104 Combinatorics and Discrete Mathematics (excl Physical Combinatorics) C1 Refereed article in a scholarly journal ©Reproduced with the specific permission of the copyright owner. http://hdl.handle.net/10536/DRO/DU:30001415