Uniformly resolvable designs with index one and block sizes three and four — with three or five parallel classes of block size four

Each parallel class of a uniformly resolvable design (URD) contains blocks of only one block size. A URD with v points and with block sizes three and four means that at least one parallel class has block size three and at least one has block size four. Danziger P. Danziger, Uniform restricted resolvable designs with r=3, ARS Combin. 46 (1997) 161-176] proved that for all there exist URDs with index one, some parallel classes of block size three, and exactly three parallel classes with block size four, except when v=12 and except possibly when . We extend Danziger’s work by showing that there exists a URD with index one, some parallel classes with block size three, and exactly three parallel classes with block size four if, and only if, , v≠12. We also prove that there exists a URD with index one, some parallel classes of block size three, and exactly five parallel classes with block size four if, and only if, , v≠12. New labeled URDs, which give new URDs as ingredient designs for recursive constructions, are the key in the proofs. Some ingredient URDs are also constructed with difference families.