Constructing designs using the union method

Given a design V, other designs can be constructed by using unions of various sets of blocks as new blocks. This method of constructing designs is referred to as "the union method". In general, the constructed design has neither constant blocksize nor balance properties. Various situations in which balanced incomplete block designs (BIBD's) and group divisible designs (GDD's) can be constructed from BIBD's and GDD's using the union method are presented. Generally speaking, it is necessary to assume that the original BIBD or GDD has a "dual property". In the cases where a BIBD V", is constructed, the question as to whether Vu is simple is considered. Simple BIBD's with less than thirty points are constructed for the following six parameter sets for which no such design was previously known: 2-(27, 12, 132), 2-(25, 7,385), 2-(27, 7, 462), 2-(27, 5,60), 2-(21, 6, 15), 2-(28, 8, 14).