Table 3 Hardening strategies corresponding to different hardening budgets of scheme 1

1

\(P_{8 - 9}^{{\text{g}}}\)

2

\(P_{1 - 2}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\)

3

\(L_{1 - 2}^{{\text{e}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(L_{14 - 15}^{{\text{h}}}\)

4

\(L_{1 - 2}^{{\text{e}}}\), \(P_{1 - 2}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(L_{14 - 15}^{{\text{h}}}\)

5

\(L_{1 - 2}^{{\text{e}}}\), \(P_{6 - 7}^{{\text{e}}}\), \(P_{1 - 2}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(L_{2 - 4}^{{\text{h}}}\)

6

\(L_{1 - 2}^{{\text{e}}}\), \(L_{6 - 26}^{{\text{e}}}\), \(P_{1 - 2}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(L_{2 - 4}^{{\text{h}}}\), \(L_{14 - 15}^{{\text{h}}}\)

7

\(L_{1 - 2}^{{\text{e}}}\), \(L_{27 - 28}^{{\text{e}}}\), \(P_{5 - 6}^{{\text{g}}}\),\(P_{8 - 9}^{{\text{g}}}\), \(P_{11 - 17}^{{\text{g}}}\), \(L_{2 - 4}^{{\text{h}}}\), \(L_{14 - 15}^{{\text{h}}}\)

8

\(L_{1 - 2}^{{\text{e}}}\), \(P_{6 - 7}^{{\text{e}}}\), \(L_{27 - 28}^{{\text{e}}}\), \(P_{5 - 6}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(P_{11 - 17}^{{\text{g}}}\), \(L_{2 - 4}^{{\text{h}}}\), \(L_{14 - 15}^{{\text{h}}}\)

9

\(L_{1 - 2}^{{\text{e}}}\), \(L_{6 - 26}^{{\text{e}}}\), \(L_{27 - 28}^{{\text{e}}}\), \(P_{1 - 2}^{{\text{g}}}\), \(P_{5 - 6}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(L_{2 - 4}^{{\text{h}}}\),\(L_{5 - 6}^{{\text{h}}}\), \(L_{14 - 15}^{{\text{h}}}\)

10

\(L_{1 - 2}^{{\text{e}}}\), \(P_{6 - 7}^{{\text{e}}}\), \(L_{6 - 26}^{{\text{e}}}\), \(P_{1 - 2}^{{\text{g}}}\), \(P_{8 - 9}^{{\text{g}}}\), \(P_{9 - 10}^{{\text{g}}}\), \(P_{11 - 17}^{{\text{g}}}\), \(L_{2 - 4}^{{\text{h}}}\), \(L_{5 - 6}^{{\text{h}}}\), \(L_{14 - 15}^{{\text{h}}}\)