A latin rectangle is an m × n array, m ≤ n, from the numbers 1, 2,. .. , n such that each of these numbers occur in each row and in each column at most once. A critical set in an m×n array is a set S of given entries, such that there exists a unique extension of S to a latin rectangle of size m×n. If we index the rows and columns of an m×n array, m ≤ n, by… (More)
In a 4-(12, 6, 4) design a block is either disjoint from one other block or it has five points in common with one other block. For a 4-(12, 6, 4) design with a pair of blocks of the second type it is shown that· another thirty blocks of the design can be completed in a unique way and these thirty blocks contain a copy of a 3-(10, 4, 1) design.
1 INTRODUCTION Given a hyperoval in a finite projective plane of even order, define an incidence structure whose point and block sets both coincide with the set of points of the plane not contained in the hyperoval and let a point and a block of the incidence structure be incident if and only if their connecting line in the projective plane intersects the… (More)