Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8: Difference between revisions
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<td rowspan="23"><math>8</math></td> | <td rowspan="23"><math>8</math></td> | ||
<td>1.1</td> | <td>1.1</td> | ||
<td>< | <td> | ||
x | <span class="htmlMath">x<sup>3</sup></span> | ||
</ | </td> | ||
<td>11818</td> | <td>11818</td> | ||
<td>420</td> | <td>420</td> | ||
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<tr> | <tr> | ||
<td>1.2</td> | <td>1.2</td> | ||
<td>< | <td> | ||
x | <span class="htmlMath">x<sup>9</sup></span> | ||
</ | </td> | ||
<td>12370</td> | <td>12370</td> | ||
<td>420</td> | <td>420</td> | ||
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<tr> | <tr> | ||
<td>1.3</td> | <td>1.3</td> | ||
<td>< | <td> | ||
x | <span class="htmlMath">x<sup>3</sup>+Tr(x<sup>9</sup>)</span> | ||
</ | </td> | ||
<td>13800</td> | <td>13800</td> | ||
<td>432</td> | <td>432</td> | ||
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<tr> | <tr> | ||
<td>1.4</td> | <td>1.4</td> | ||
<td>< | <td> | ||
x | <span class="htmlMath">x<sup>9</sup>+Tr(x<sup>3</sup>)</span> | ||
</ | </td> | ||
<td>13804</td> | <td>13804</td> | ||
<td>434</td> | <td>434</td> | ||
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<tr> | <tr> | ||
<td>1.5</td> | <td>1.5</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup>+u<sup>245</sup>x<sup>33</sup>+u<sup>183</sup>x<sup>66</sup>+u<sup>21</sup>x<sup>144</sup></span></td> | ||
x | |||
</ | |||
<td>13842</td> | <td>13842</td> | ||
<td>436</td> | <td>436</td> | ||
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<tr> | <tr> | ||
<td>1.6</td> | <td>1.6</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup> + u<sup>65</sup>x<sup>18</sup>+u<sup>120</sup>x<sup>66</sup>+u<sup>135</sup>x<sup>144</sup></span></td> | ||
x | |||
</ | |||
<td>13848</td> | <td>13848</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.7</td> | <td>1.7</td> | ||
<td>< | <td><span class="htmlMath">u<sup>188</sup>x<sup>192</sup> + u<sup>129</sup>x<sup>144</sup> + u<sup>172</sup>x<sup>132</sup> + u<sup>138</sup>x<sup>129</sup> + u<sup>74</sup>x<sup>96</sup> + u<sup>244</sup>x<sup>72</sup> + u<sup>22</sup>x<sup>66</sup> + u<sup>178</sup>x<sup>48</sup> + u<sup>150</sup>x<sup>36</sup> + u<sup>146</sup>x<sup>33</sup> + u<sup>6</sup>x<sup>24</sup> + u<sup>60</sup>x<sup>18</sup> + u<sup>80</sup>x<sup>12</sup> + u<sup>140</sup>x<sup>9</sup> + u<sup>221</sup>x<sup>6</sup> + u<sup>19</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14034</td> | <td>14034</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.8</td> | <td>1.8</td> | ||
<td>< | <td><span class="htmlMath">u<sup>37</sup>x<sup>192</sup> + u<sup>110</sup>x<sup>144</sup> + u<sup>40</sup>x<sup>132</sup> + u<sup>53</sup>x<sup>129</sup> + u<sup>239</sup>x<sup>96</sup> + u<sup>235</sup>x<sup>72</sup> + u<sup>126</sup>x<sup>66</sup> + u<sup>215</sup>x<sup>48</sup> + u<sup>96</sup>x<sup>36</sup> + u<sup>29</sup>x<sup>33</sup> + u<sup>19</sup>x<sup>24</sup> + u<sup>14</sup>x<sup>18</sup> + u<sup>139</sup>x<sup>12</sup> + u<sup>230</sup>x<sup>9</sup> + u<sup>234</sup>x<sup>6</sup> + u<sup>228</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14032</td> | <td>14032</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.9</td> | <td>1.9</td> | ||
<td>< | <td><span class="htmlMath">u<sup>242</sup>x<sup>192</sup> + u<sup>100</sup>x<sup>144</sup> + u<sup>66</sup>x<sup>132</sup> + u<sup>230</sup>x<sup>129</sup> + u<sup>202</sup>x<sup>96</sup> + u<sup>156</sup>x<sup>72</sup> + u<sup>254</sup>x<sup>66</sup> + u<sup>18</sup>x<sup>48</sup> + u<sup>44</sup>x<sup>36</sup> + u<sup>95</sup>x<sup>33</sup> + u<sup>100</sup>x<sup>24</sup> + u<sup>245</sup>x<sup>18</sup> + u<sup>174</sup>x<sup>12</sup> + u<sup>175</sup>x<sup>9</sup> + u<sup>247</sup>x<sup>6</sup> + u<sup>166</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14036</td> | <td>14036</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.10</td> | <td>1.10</td> | ||
<td>< | <td><span class="htmlMath">u<sup>100</sup>x<sup>192</sup> + u<sup>83</sup>x<sup>144</sup> + u<sup>153</sup>x<sup>132</sup> + u<sup>65</sup>x<sup>129</sup> + u<sup>174</sup>x<sup>96</sup> + u<sup>136</sup>x<sup>72</sup> + u<sup>46</sup>x<sup>66</sup>+ u<sup>55</sup>x<sup>48</sup>+ u<sup>224</sup>x<sup>36</sup>+ u<sup>180</sup>x<sup>33</sup>+ u<sup>179</sup>x<sup>24</sup>+u<sup>226</sup>x<sup>18</sup>+ u<sup>54</sup>x<sup>12</sup>+ u<sup>168</sup>x<sup>9</sup>+ u<sup>89</sup>x<sup>6</sup>+ u<sup>56</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14036</td> | <td>14036</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.11</td> | <td>1.11</td> | ||
<td>< | <td><span class="htmlMath">u<sup>77</sup>x<sup>192</sup> + u<sup>133</sup>x<sup>144</sup> + u<sup>47</sup>x<sup>132</sup> + u<sup>229</sup>x<sup>129</sup> + u<sup>23</sup>x<sup>96</sup> + u<sup>242</sup>x<sup>72</sup> + u<sup>242</sup>x<sup>66</sup> + u<sup>245</sup>x<sup>48</sup> + u<sup>212</sup>x<sup>36</sup> + u<sup>231</sup>x<sup>33</sup> + u<sup>174</sup>x<sup>24</sup> + u<sup>216</sup>x<sup>18</sup> + u<sup>96</sup>x<sup>12</sup> + u<sup>253</sup>x<sup>9</sup> + u<sup>154</sup>x<sup>6</sup> + u<sup>71</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14032</td> | <td>14032</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.12</td> | <td>1.12</td> | ||
<td>< | <td><span class="htmlMath">u<sup>220</sup>x<sup>192</sup> + u<sup>94</sup>x<sup>144</sup> + u<sup>70</sup>x<sup>132</sup> + u<sup>159</sup>x<sup>129</sup> + u<sup>145</sup>x<sup>96</sup> + u<sup>160</sup>x<sup>72</sup> + u<sup>74</sup>x<sup>66</sup> + u<sup>184</sup>x<sup>48</sup> + u<sup>119</sup>x<sup>36</sup> + u<sup>106</sup>x<sup>33</sup> + u<sup>253</sup>x<sup>24</sup> + wx<sup>18</sup> + u<sup>90</sup>x<sup>12</sup> + u<sup>169</sup>x<sup>9</sup> + u<sup>118</sup>x<sup>6</sup> + u<sup>187</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14034</td> | <td>14034</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.13</td> | <td>1.13</td> | ||
<td>< | <td><span class="htmlMath">u<sup>98</sup>x<sup>192</sup> + u<sup>225</sup>x<sup>144</sup> + u<sup>111</sup>x<sup>132</sup> + u<sup>238</sup>x<sup>129</sup> + u<sup>182</sup>x<sup>96</sup> + u<sup>125</sup>x<sup>72</sup> + u<sup>196</sup>x<sup>66</sup> + u<sup>219</sup>x<sup>48</sup> + u<sup>189</sup>x<sup>36</sup> + u<sup>199</sup>x<sup>33</sup> + u<sup>181</sup>x<sup>24</sup> + u<sup>110</sup>x<sup>18</sup> + u<sup>19</sup>x<sup>12</sup> + u<sup>175</sup>x<sup>9</sup> + u<sup>133</sup>x<sup>6</sup> + u<sup>47</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14030</td> | <td>14030</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.14</td> | <td>1.14</td> | ||
<td>< | <td><span class="htmlMath">u<sup>236</sup>x<sup>192</sup> + u<sup>212</sup>x<sup>160</sup> + u<sup>153</sup>x<sup>144</sup> + u<sup>185</sup>x<sup>136</sup> + u<sup>3</sup>x<sup>132</sup> + u<sup>89</sup>x<sup>130</sup> + u<sup>189</sup>x<sup>129</sup> + u<sup>182</sup>x<sup>96</sup> + u<sup>105</sup>x<sup>80</sup> + u<sup>232</sup>x<sup>72</sup> + u<sup>219</sup>x<sup>68</sup> + u<sup>145</sup>x<sup>66</sup> + u<sup>171</sup>x<sup>65</sup> + u<sup>107</sup>x<sup>48</sup> + u<sup>179</sup>x<sup>40</sup> + u<sup>227</sup>x<sup>36</sup> + u<sup>236</sup>x<sup>34</sup> + u<sup>189</sup>x<sup>33</sup> + u<sup>162</sup>x<sup>24</sup> + u<sup>216</sup>x<sup>20</sup> + u<sup>162</sup>x<sup>18</sup> + u<sup>117</sup>x<sup>17</sup> + u<sup>56</sup>x<sup>12</sup> + u<sup>107</sup>x<sup>10</sup> + u<sup>236</sup>x<sup>9</sup> + u<sup>253</sup>x<sup>6</sup> + u<sup>180</sup>x<sup>5</sup> + u<sup>18</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14046</td> | <td>14046</td> | ||
<td>454</td> | <td>454</td> | ||
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<tr> | <tr> | ||
<td>1.15</td> | <td>1.15</td> | ||
<td>< | <td><span class="htmlMath">u<sup>27</sup>x<sup>192</sup> + u<sup>167</sup>x<sup>144</sup> + u<sup>26</sup>x<sup>132</sup> + u<sup>231</sup>x<sup>129</sup> + u<sup>139</sup>x<sup>96</sup> + u<sup>30</sup>x<sup>72</sup> + u<sup>139</sup>x<sup>66</sup> + u<sup>203</sup>x<sup>48</sup> + u<sup>36</sup>x<sup>36</sup> + u<sup>210</sup>x<sup>33</sup> + u<sup>195</sup>x<sup>24</sup> + u<sup>12</sup>x<sup>18</sup> + u<sup>43</sup>x<sup>12</sup> + u<sup>97</sup>x<sup>9</sup> + u<sup>61</sup>x<sup>6</sup> + u<sup>39</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14036</td> | <td>14036</td> | ||
<td>454</td> | <td>454</td> | ||
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<tr> | <tr> | ||
<td>1.16</td> | <td>1.16</td> | ||
<td>< | <td><span class="htmlMath">u<sup>6</sup>x<sup>192</sup> + u<sup>85</sup>x<sup>144</sup> + u<sup>251</sup>x<sup>132</sup> + u<sup>215</sup>x<sup>129</sup> + u<sup>229</sup>x<sup>96</sup> + u<sup>195</sup>x<sup>72</sup> + u<sup>152</sup>x<sup>66</sup> + u<sup>173</sup>x<sup>48</sup> + u<sup>209</sup>x<sup>36</sup> + u<sup>165</sup>x<sup>33</sup> + u<sup>213</sup>x<sup>24</sup> + u<sup>214</sup>x<sup>18</sup> + u<sup>158</sup>x<sup>12</sup> + u<sup>146</sup>x<sup>9</sup> + x<sup>6</sup> + u<sup>50</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14032</td> | <td>14032</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>1.17</td> | <td>1.17</td> | ||
<td>< | <td><span class="htmlMath">u<sup>164</sup>x<sup>192</sup> + u<sup>224</sup>x<sup>144</sup> + u<sup>59</sup>x<sup>132</sup> + u<sup>124</sup>x<sup>129</sup> + u<sup>207</sup>x<sup>96</sup> + u<sup>211</sup>x<sup>72</sup> + u<sup>5</sup>x<sup>66</sup> + u<sup>26</sup>x<sup>48</sup> + u<sup>20</sup>x<sup>36</sup> + u<sup>101</sup>x<sup>33</sup> + u<sup>175</sup>x<sup>24</sup> + u<sup>241</sup>x<sup>18</sup> + x<sup>12</sup> + u<sup>15</sup>x<sup>9</sup> + u<sup>217</sup>x<sup>6</sup> + u<sup>212</sup>x<sup>3</sup></span></td> | ||
u | |||
</ | |||
<td>14028</td> | <td>14028</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>2.1</td> | <td>2.1</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup>+ x<sup>17</sup>+u<sup>16</sup>(x<sup>18</sup>+x<sup>33</sup>)+u<sup>15</sup>x<sup>48</sup></span></td> | ||
x | |||
</ | |||
<td>13200</td> | <td>13200</td> | ||
<td>414</td> | <td>414</td> | ||
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<tr> | <tr> | ||
<td>3.1</td> | <td>3.1</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup>+ u<sup>24</sup>x<sup>6</sup>+u<sup>182</sup>x<sup>132</sup>+u<sup>67</sup>x<sup>192</sup></span></td> | ||
x | |||
</ | |||
<td>14024</td> | <td>14024</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>4.1</td> | <td>4.1</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup>+x<sup>6</sup>+x<sup>68</sup>+x<sup>80</sup>+x<sup>132</sup>+x<sup>160</sup></span></td> | ||
x | |||
</ | |||
<td>14040</td> | <td>14040</td> | ||
<td>454</td> | <td>454</td> | ||
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<tr> | <tr> | ||
<td>5.1</td> | <td>5.1</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup>+x<sup>5</sup>+x<sup>18</sup>+x<sup>40</sup>+x<sup>66</sup></span></td> | ||
x | |||
</ | |||
<td>14044</td> | <td>14044</td> | ||
<td>446</td> | <td>446</td> | ||
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<tr> | <tr> | ||
<td>6.1</td> | <td>6.1</td> | ||
<td>< | <td><span class="htmlMath">x<sup>3</sup>+x<sup>12</sup>+x<sup>40</sup>+x<sup>66</sup>+x<sup>130</sup></span></td> | ||
x | |||
</ | |||
<td>14046</td> | <td>14046</td> | ||
<td>438</td> | <td>438</td> | ||
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<tr> | <tr> | ||
<td>7.1</td> | <td>7.1</td> | ||
<td>< | <td> | ||
x | <span class="htmlMath">x<sup>57</sup></span> | ||
</ | </td> | ||
<td>15358</td> | <td>15358</td> | ||
<td>960</td> | <td>960</td> |
Revision as of 17:52, 11 July 2020
Known switching classes of APN functions over [math]\displaystyle{ \mathbb{F}_{2^5} }[/math], [math]\displaystyle{ \mathbb{F}_{2^6} }[/math], [math]\displaystyle{ \mathbb{F}_{2^7} }[/math] and [math]\displaystyle{ \mathbb{F}_{2^8} }[/math].
Also available is Magma code generating representatives from the switching classes.
[math]\displaystyle{ n }[/math] | [math]\displaystyle{ N^\circ }[/math] | [math]\displaystyle{ F(x) }[/math] | Γ-rank | Δ-rank | Aut(dev(GF))/22n | Aut(dev(GF))/22n |
---|---|---|---|---|---|---|
[math]\displaystyle{ 5 }[/math] | 1.1 | x3 | 330 | 42 | 4960 | 4960 |
1.2 | x5 | 330 | 42 | 4960 | 158720 | |
2.1 | x-1 | 496 | 232 | 310 | 310 | |
[math]\displaystyle{ 6 }[/math] | 1.1 | x3 | 1102 | 94 | 24192 | 48384 |
1.2 | x3 + u11x6 + ux9 | 1146 | 94 | 4032 | 8064 | |
2.1 | ux5 + x9 + u4x17 + ux18 + u4x20 + ux24 + u4x34 + ux40 | 1158 | 96 | 320 | 320 | |
2.2 | u7x3 + x5 + u3x9 + u4x10 + x17 + u6x18 | 1166 | 94 | 448 | 896 | |
2.3 | x3 + ux24 + x10 | 1166 | 96 | 896 | 896 | |
2.4 | x3 + u17(x17 + x18 + x20 + x24) | 1168 | 96 | 64 | 64 | |
2.5 | x3 + u11x5 + u13x9 + x17 + u11x33 + x48 | 1170 | 96 | 320 | 320 | |
2.6 | u25x5 + x9 + u38x12 + u25x18 + u25x36 | 1170 | 96 | 64 | 64 | |
2.7 | u40x5 + u10x6 + u62x20 + u35x33 + u15x34 + u29x48 | 1170 | 96 | 64 | 64 | |
2.8 | u34x6 + u52x9 + u48x12 + u6x20 + u9x33 + u23x34 + u25x40 | 1170 | 96 | 64 | 64 | |
2.9 | x9 + u4(x10 + x18) + u9(x12 + x20 + x40) | 1172 | 96 | 64 | 64 | |
2.10 | u52x3 + u47x5 + ux6 + u9x9 + u44x12 + u47x33 + u10x34 + u33x40 | 1172 | 96 | 64 | 64 | |
2.11 | u(x6 + x10 + x24 + x33) + x9 + u4x17 | 1174 | 96 | 64 | 64 | |
2.12 | x3 + u17(x17 + x18 + x20 + x24) + u14((u52x3 + u6x5 + u19x7 + u28x11 + u2x13)+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)2 + (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)4+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)8+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)16+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)32+ (u2x)9 +(u2x)19 +(u2x)36 + x21+x42 | 1300 | 152 | 8 | 8 | |
[math]\displaystyle{ 7 }[/math] | 1.1 |
x3 |
3610 | 198 | 113792 | 113792 |
1.2 |
x3 + Tr(x9) |
4026 | 212 | 896 | 896 | |
2.1 |
x34 + x18 + x5 |
4034 | 210 | 896 | 896 | |
2.2 |
x3 + x17 + x33 + x34 |
4040 | 212 | 896 | 896 | |
3.1 |
x5 |
3708 | 198 | 113792 | 113792 | |
4.1 |
x9 |
3610 | 198 | 113792 | 14565376 | |
5.1 |
x13 |
4270 | 338 | 889 | 889 | |
6.1 |
x57 |
4704 | 436 | 889 | 889 | |
7.1 |
x-1 |
8128 | 4928 | 1778 | 1778 | |
8.1 |
x65 + x10 + x3 |
4038 | 212 | 896 | 896 | |
9.1 |
x3 + x9 + x18 + x66 |
4044 | 212 | 896 | 896 | |
10.1 |
x3 + x12 + x17 + x33 |
4048 | 210 | 896 | 896 | |
10.2 |
x3 + x17 + x20 + x34 + x66 |
4040 | 210 | 896 | 896 | |
11.1 |
x3 + x20 + x34 + x66 |
4048 | 210 | 896 | 896 | |
12.1 |
x3 + x12 + x40 + x72 |
4048 | 210 | 896 | 896 | |
13.1 |
x3 + x5 + x10 + x33 + x34 |
4040 | 212 | 896 | 896 | |
14.1 |
x3 + x6 + x34 + x40 + x72 |
4048 | 212 | 896 | 896 | |
14.2 |
x3 + x5 + x6 + x12 + x33 + x34 |
4050 | 210 | 896 | 896 | |
14.3 |
u2x96 + u78x80 + u121x72 + u49x68 + u77x66 + u29x65 + u119x48 + u117x40 + u28x36 + u107x34 +u62x33 +u125x24 +u76x20 +u84x18 +u110x17 +u49x12 +u102x10 +u69x9 + u14x6 + x5 + x3 |
4046 | 212 | 128 | 128 | |
[math]\displaystyle{ 8 }[/math] | 1.1 |
x3 |
11818 | 420 | ||
1.2 |
x9 |
12370 | 420 | |||
1.3 |
x3+Tr(x9) |
13800 | 432 | |||
1.4 |
x9+Tr(x3) |
13804 | 434 | |||
1.5 | x3+u245x33+u183x66+u21x144 | 13842 | 436 | |||
1.6 | x3 + u65x18+u120x66+u135x144 | 13848 | 438 | |||
1.7 | u188x192 + u129x144 + u172x132 + u138x129 + u74x96 + u244x72 + u22x66 + u178x48 + u150x36 + u146x33 + u6x24 + u60x18 + u80x12 + u140x9 + u221x6 + u19x3 | 14034 | 438 | |||
1.8 | u37x192 + u110x144 + u40x132 + u53x129 + u239x96 + u235x72 + u126x66 + u215x48 + u96x36 + u29x33 + u19x24 + u14x18 + u139x12 + u230x9 + u234x6 + u228x3 | 14032 | 438 | |||
1.9 | u242x192 + u100x144 + u66x132 + u230x129 + u202x96 + u156x72 + u254x66 + u18x48 + u44x36 + u95x33 + u100x24 + u245x18 + u174x12 + u175x9 + u247x6 + u166x3 | 14036 | 438 | |||
1.10 | u100x192 + u83x144 + u153x132 + u65x129 + u174x96 + u136x72 + u46x66+ u55x48+ u224x36+ u180x33+ u179x24+u226x18+ u54x12+ u168x9+ u89x6+ u56x3 | 14036 | 438 | |||
1.11 | u77x192 + u133x144 + u47x132 + u229x129 + u23x96 + u242x72 + u242x66 + u245x48 + u212x36 + u231x33 + u174x24 + u216x18 + u96x12 + u253x9 + u154x6 + u71x3 | 14032 | 438 | |||
1.12 | u220x192 + u94x144 + u70x132 + u159x129 + u145x96 + u160x72 + u74x66 + u184x48 + u119x36 + u106x33 + u253x24 + wx18 + u90x12 + u169x9 + u118x6 + u187x3 | 14034 | 438 | |||
1.13 | u98x192 + u225x144 + u111x132 + u238x129 + u182x96 + u125x72 + u196x66 + u219x48 + u189x36 + u199x33 + u181x24 + u110x18 + u19x12 + u175x9 + u133x6 + u47x3 | 14030 | 438 | |||
1.14 | u236x192 + u212x160 + u153x144 + u185x136 + u3x132 + u89x130 + u189x129 + u182x96 + u105x80 + u232x72 + u219x68 + u145x66 + u171x65 + u107x48 + u179x40 + u227x36 + u236x34 + u189x33 + u162x24 + u216x20 + u162x18 + u117x17 + u56x12 + u107x10 + u236x9 + u253x6 + u180x5 + u18x3 | 14046 | 454 | |||
1.15 | u27x192 + u167x144 + u26x132 + u231x129 + u139x96 + u30x72 + u139x66 + u203x48 + u36x36 + u210x33 + u195x24 + u12x18 + u43x12 + u97x9 + u61x6 + u39x3 | 14036 | 454 | |||
1.16 | u6x192 + u85x144 + u251x132 + u215x129 + u229x96 + u195x72 + u152x66 + u173x48 + u209x36 + u165x33 + u213x24 + u214x18 + u158x12 + u146x9 + x6 + u50x3 | 14032 | 438 | |||
1.17 | u164x192 + u224x144 + u59x132 + u124x129 + u207x96 + u211x72 + u5x66 + u26x48 + u20x36 + u101x33 + u175x24 + u241x18 + x12 + u15x9 + u217x6 + u212x3 | 14028 | 438 | |||
2.1 | x3+ x17+u16(x18+x33)+u15x48 | 13200 | 414 | |||
3.1 | x3+ u24x6+u182x132+u67x192 | 14024 | 438 | |||
4.1 | x3+x6+x68+x80+x132+x160 | 14040 | 454 | |||
5.1 | x3+x5+x18+x40+x66 | 14044 | 446 | |||
6.1 | x3+x12+x40+x66+x130 | 14046 | 438 | |||
7.1 |
x57 |
15358 | 960 |