Classification of resolvable balanced incomplete block designs - The unitals on 28 points

Abstract

Approaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type - and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder - it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points. © 2009 © Versita Warsaw and Springer-Verlag Berlin Heidelberg.