BIBD's with block-size seven (Q1823944)

This paper is an addition to \textit{H. Hanani} [Balanced incomplete block designs and related designs, Discrete Math. 11, 255-269 (1975; Zbl 0361.62067)] and uses the numbering system from the preceding paper. The author proves that the obvious necessary conditions for the existence of a BIBD with \(k=7\) and \(\lambda =3\) and 21 are sufficient, with the possible exception of the values \(\lambda =3\) and \(v=323\), 351, 407, 519, 525, 575 and 665.