ABSTRACT
The first block designs to be studied in detail were BIBDs with block size 3. These are also called triple systems, and the words “block” and “triple” are used interchangeably.
In 1844 Woolhouse [181] asked about block designs with λ = 1; in 1845 [182] he reported a lack of solutions, and in 1846 [183] he simplified the problem to the case of triple systems, and gave some further comments the following year [184]. Meanwhile Kirkman solved the existence problem for triple systems in a lecture to the Royal Society; this was published in 1847 [88]. In 1853 Steiner [140] discussed t-designs with k = t+1 and λ = 1; when t = 2 these are triple systems with λ = 1, so they are called Steiner triple systems.
