Table 1 Exact values of \(\Gamma_{m}(\Delta)\) (cf. [11, p. 333]) and \(\Gamma_{m}(T)\) (cf. [9, p. 2559]) and consequences of Theorem 4 for \(\Gamma_{m}(C)\) with \(C = T\)

m

3

4

5

6

7

8

\(\Gamma_{m}(\Delta)\)

\(\frac{2}{3}\)

\(\frac{4}{7}\)

\(\frac {8}{15}\)

\(\frac{1}{2}\)

\(\frac{5}{11}\)

\(\frac{3}{7}\)

\(\Gamma_{m}(T)\)

1

\(\frac{3}{4}\)

\(\frac{9}{13}\)

–

–

–

\(\Gamma_{m}(C)\)

1

\({\leq}\frac{3}{4}\)

\({\leq}\frac{7}{10}\)

\({\leq}\frac{15}{22}\)

\({\leq}\frac{2}{3}\)

\({\leq}\frac{11}{17}\)