Blocking sets of 16 points in projective planes of order 10. III (Q1076969)

Let \(\Pi\) be a finite projective plane of order 10 with line-set L, and let B be a blocking set of \(\Pi\). Denote by \(a_ i\) the number of lines of \(\Pi\) intersecting B in i points. The case \(| B| =15\) has been ruled out by \textit{R. H. F. Denniston} [J. Aust. Math. Soc. 10, 214-218 (1969; Zbl 0175.477)]. The author considers \(| B| =16\); then for \(i>6\) is \(a_ i=0\). The case \(a_ 6\neq 0\) has been ruled out by the author with the help of a computerprogram [cf. part I (unpublished) and part II, Q. J. Math., Oxf. II. Ser. 36, 383-391 (1985; Zbl 0591.51013) of the present paper]. In the present paper it is proved that one of the following holds: \(a_ 5=6\), \(a_ 4=4\), \(a_ 3=7\), \(a_ 2=15\).