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

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. <br /

More mutually orthogonal latin squares

AbstractWilson's construction for mutually orthogonal Latin squares is generalized. This generalized construction is used to improve known bounds on the function nr (the largest order for which there do not exist r MOLS). In particular we find n7⩽780, n8⩽4738, n9⩽5842, n10⩽7222, n11⩽7478, n12⩽9286, n13⩽9476, n15⩽10632

A series of separable designs with application to pairwise orthogonal Latin squares

We observe that a partitien of PG(2, q2) into Baer subplanes gives rise to certain separable pairwise balanced block designs (with ¿ = 1) which in turn can be used to get more mutually orthogonal Latin squares of certain orders than previously known. As a side result we find an embedding of STS(19) in PG(2, 11), thus refuting a conjecture of M. Limbos

A series of separable designs with application to pairwise orthogonal Latin squares

We observe that a partitien of PG(2, q2) into Baer subplanes gives rise to certain separable pairwise balanced block designs (with ¿ = 1) which in turn can be used to get more mutually orthogonal Latin squares of certain orders than previously known. As a side result we find an embedding of STS(19) in PG(2, 11), thus refuting a conjecture of M. Limbos

A series of separable designs with application to pairwise orthogonal Latin squares

We observe that a partitien of PG(2, q2) into Baer subplanes gives rise to certain separable pairwise balanced block designs (with ¿ = 1) which in turn can be used to get more mutually orthogonal Latin squares of certain orders than previously known. As a side result we find an embedding of STS(19) in PG(2, 11), thus refuting a conjecture of M. Limbos