Unital designs in planes of order 16
A unital is any \(2\)-\((q^3 + 1, q + 1, 1)\) design. The classical example of a unital is an Hermitian curve embedded in \(\text{PG}(2, q^2)\). It should be noted that not all unitals of order \(q\) are embedded in projective planes of order \(q^2\). For the paper under review the authors search (non-exhaustively) for unitals embedded in the known planes of order 16. A total of 38 (inequivalent) unitals were found, and each of the known planes of order 16 contains at least one unital. The resulting 38 designs are mutually non-isomorphic as designs. Thus the total of known non-isomorphic \(2\)-\((65, 5, 1)\) designs is now 40, and 15 of these are resolvable.
scientific article; zbMATH DE number 1436250