Maximal arc partitions of designs
An \(\alpha\)-arc in a 2-design is a subset of points that meets every block in either 0 or \(\alpha\) points, and an \(\alpha\)-spread is a collection of \(\alpha\)-arcs that partitions the point set. An \(\alpha\)-arc is called symmetric if the induced design on it is a multiple of a symmetric design, and an \(\alpha\)-spread is called symmetric if all \(\alpha\)-arcs contained in it are symmetric. The authors show that there exists a complementary Hadamard 2-\((\mu m^ 2 -1, {1 \over 2}\mu m^ 2, {1 \over 4}\mu m^ 2)\) design admitting a \({1 \over 2}m\)-spread if and only if there exists an affine 2-\((\mu m^ 2, \mu m, (\mu m -1)/(m-1))\) design and a complementary Hadamard 2-\((m-1, {1 \over 2}m, {1 \over 4}m)\) design.
scientific article; zbMATH DE number 2182125