Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8: Difference between revisions
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Known switching classes of APN functions over < | Known switching classes of APN functions over <span class="htmlMath">GF(2<sup>5</sup>), GF(2<sup>6</sup>), GF(2<sup>7</sup>)</span> and <span class="htmlMath">GF(2<sup>8</sup>)</span>. | ||
Also available is [[:File:switching_classes.txt|Magma code generating representatives from the switching classes]]. | Also available is [[:File:switching_classes.txt|Magma code generating representatives from the switching classes]]. | ||
Line 5: | Line 5: | ||
<table> | <table> | ||
<tr> | <tr> | ||
<th>< | <th><span class="htmlMath">n</span></th> | ||
<th>< | <th><span class="htmlMath">N</span></th> | ||
<th>< | <th><span class="htmlMath">F(x)</span></th> | ||
<th>Γ-rank</th> | <th>Γ-rank</th> | ||
<th>Δ-rank</th> | <th>Δ-rank</th> | ||
<th>Aut(dev(G<sub>F</sub>))/2<sup>2n</sup></th> | <th>Aut(dev(G<sub>F</sub>))/2<sup>2n</sup></th> | ||
<th>Aut(dev(G<sub>F</sub>))/2<sup>2n</sup></th> | <th>Aut(dev(G<sub>F</sub>))/2<sup>2n</sup></th> | ||
<th>Multiplier group</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td rowspan="3" | <td rowspan="3">5</td> | ||
<td>1.1</td> | <td>1.1</td> | ||
<td><span class="htmlMath">x<sup>3</sup></span></td> | <td><span class="htmlMath">x<sup>3</sup></span></td> | ||
<td>330</td> | <td>330</td> | ||
<td>42</td> | <td>42</td> | ||
<td>4960</td> | |||
<td>4960</td> | <td>4960</td> | ||
<td>4960</td> | <td>4960</td> | ||
Line 29: | Line 31: | ||
<td>4960</td> | <td>4960</td> | ||
<td>158720</td> | <td>158720</td> | ||
<td>4960</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 35: | Line 38: | ||
<td>496</td> | <td>496</td> | ||
<td>232</td> | <td>232</td> | ||
<td>310</td> | |||
<td>310</td> | <td>310</td> | ||
<td>310</td> | <td>310</td> | ||
Line 40: | Line 44: | ||
</tr> | </tr> | ||
<tr class="strongDivider"> | <tr class="strongDivider"> | ||
<td rowspan="14" | <td rowspan="14">6</td> | ||
<td>1.1</td> | <td>1.1</td> | ||
<td><span class="htmlMath">x<sup>3</sup></span></td> | <td><span class="htmlMath">x<sup>3</sup></span></td> | ||
Line 47: | Line 51: | ||
<td>24192</td> | <td>24192</td> | ||
<td>48384</td> | <td>48384</td> | ||
<td>24192</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 55: | Line 60: | ||
<td>4032</td> | <td>4032</td> | ||
<td>8064</td> | <td>8064</td> | ||
<td>4032</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 61: | Line 67: | ||
<td>1158</td> | <td>1158</td> | ||
<td>96</td> | <td>96</td> | ||
<td>320</td> | |||
<td>320</td> | <td>320</td> | ||
<td>320</td> | <td>320</td> | ||
Line 71: | Line 78: | ||
<td>448</td> | <td>448</td> | ||
<td>896</td> | <td>896</td> | ||
<td>448</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 77: | Line 85: | ||
<td>1166</td> | <td>1166</td> | ||
<td>96</td> | <td>96</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 85: | Line 94: | ||
<td>1168</td> | <td>1168</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 93: | Line 103: | ||
<td>1170</td> | <td>1170</td> | ||
<td>96</td> | <td>96</td> | ||
<td>320</td> | |||
<td>320</td> | <td>320</td> | ||
<td>320</td> | <td>320</td> | ||
Line 101: | Line 112: | ||
<td>1170</td> | <td>1170</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 109: | Line 121: | ||
<td>1170</td> | <td>1170</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 117: | Line 130: | ||
<td>1170</td> | <td>1170</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 125: | Line 139: | ||
<td>1172</td> | <td>1172</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 133: | Line 148: | ||
<td>1172</td> | <td>1172</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 141: | Line 157: | ||
<td>1174</td> | <td>1174</td> | ||
<td>96</td> | <td>96</td> | ||
<td>64</td> | |||
<td>64</td> | <td>64</td> | ||
<td>64</td> | <td>64</td> | ||
Line 146: | Line 163: | ||
<tr> | <tr> | ||
<td>2.12</td> | <td>2.12</td> | ||
<td><span class="htmlMath">x<sup>3</sup> + u<sup>17</sup>(x<sup>17</sup> + x<sup>18</sup> + x<sup>20</sup> + x<sup>24</sup>) + u<sup>14</sup> | <td><span class="htmlMath">x<sup>3</sup> + u<sup>17</sup>(x<sup>17</sup> + x<sup>18</sup> + x<sup>20</sup> + x<sup>24</sup>) + u<sup>14</sup>(u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>2</sup> + (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>4</sup>+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>8</sup>+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>16</sup>+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>32</sup>+ (u<sup>2</sup>x)<sup>9</sup> +(u<sup>2</sup>x)<sup>19</sup> +(u<sup>2</sup>x)<sup>36</sup> + x<sup>21</sup>+x<sup>42</sup></span></td> | ||
<td>1300</td> | <td>1300</td> | ||
<td>152</td> | <td>152</td> | ||
<td>8</td> | |||
<td>8</td> | <td>8</td> | ||
<td>8</td> | <td>8</td> | ||
</tr> | </tr> | ||
<tr class="strongDivider"> | <tr class="strongDivider"> | ||
<td rowspan="19" | <td rowspan="19">7</td> | ||
<td>1.1</td> | <td>1.1</td> | ||
<td> | <td> | ||
Line 160: | Line 178: | ||
<td>3610</td> | <td>3610</td> | ||
<td>198</td> | <td>198</td> | ||
<td>113792</td> | |||
<td>113792</td> | <td>113792</td> | ||
<td>113792</td> | <td>113792</td> | ||
Line 170: | Line 189: | ||
<td>4026</td> | <td>4026</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 180: | Line 200: | ||
<td>4034</td> | <td>4034</td> | ||
<td>210</td> | <td>210</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 190: | Line 211: | ||
<td>4040</td> | <td>4040</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 200: | Line 222: | ||
<td>3708</td> | <td>3708</td> | ||
<td>198</td> | <td>198</td> | ||
<td>113792</td> | |||
<td>113792</td> | <td>113792</td> | ||
<td>113792</td> | <td>113792</td> | ||
Line 212: | Line 235: | ||
<td>113792</td> | <td>113792</td> | ||
<td>14565376</td> | <td>14565376</td> | ||
<td>113792</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 220: | Line 244: | ||
<td>4270</td> | <td>4270</td> | ||
<td>338</td> | <td>338</td> | ||
<td>889</td> | |||
<td>889</td> | <td>889</td> | ||
<td>889</td> | <td>889</td> | ||
Line 230: | Line 255: | ||
<td>4704</td> | <td>4704</td> | ||
<td>436</td> | <td>436</td> | ||
<td>889</td> | |||
<td>889</td> | <td>889</td> | ||
<td>889</td> | <td>889</td> | ||
Line 240: | Line 266: | ||
<td>8128</td> | <td>8128</td> | ||
<td>4928</td> | <td>4928</td> | ||
<td>1778</td> | |||
<td>1778</td> | <td>1778</td> | ||
<td>1778</td> | <td>1778</td> | ||
Line 250: | Line 277: | ||
<td>4038</td> | <td>4038</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 260: | Line 288: | ||
<td>4044</td> | <td>4044</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 270: | Line 299: | ||
<td>4048</td> | <td>4048</td> | ||
<td>210</td> | <td>210</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 280: | Line 310: | ||
<td>4040</td> | <td>4040</td> | ||
<td>210</td> | <td>210</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 290: | Line 321: | ||
<td>4048</td> | <td>4048</td> | ||
<td>210</td> | <td>210</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 300: | Line 332: | ||
<td>4048</td> | <td>4048</td> | ||
<td>210</td> | <td>210</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 310: | Line 343: | ||
<td>4040</td> | <td>4040</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 320: | Line 354: | ||
<td>4048</td> | <td>4048</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 330: | Line 365: | ||
<td>4050</td> | <td>4050</td> | ||
<td>210</td> | <td>210</td> | ||
<td>896</td> | |||
<td>896</td> | <td>896</td> | ||
<td>896</td> | <td>896</td> | ||
Line 340: | Line 376: | ||
<td>4046</td> | <td>4046</td> | ||
<td>212</td> | <td>212</td> | ||
<td>128</td> | |||
<td>128</td> | <td>128</td> | ||
<td>128</td> | <td>128</td> | ||
</tr> | </tr> | ||
<tr class="strongDivider"> | <tr class="strongDivider"> | ||
<td rowspan="23" | <td rowspan="23">8</td> | ||
<td>1.1</td> | <td>1.1</td> | ||
<td> | <td> | ||
Line 353: | Line 390: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>522240</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 363: | Line 401: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>522240</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 373: | Line 412: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>6144</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 383: | Line 423: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>6144</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 391: | Line 432: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 399: | Line 442: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 407: | Line 451: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>768</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 415: | Line 460: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 423: | Line 469: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 431: | Line 478: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>1536</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 439: | Line 487: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 447: | Line 496: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 455: | Line 505: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>1536</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 463: | Line 514: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>512</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 471: | Line 523: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>768</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 479: | Line 532: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>1536</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 487: | Line 541: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>1536</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 495: | Line 550: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>46080</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 503: | Line 559: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>3072</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 511: | Line 568: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>2048</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 519: | Line 577: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>2048</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 527: | Line 586: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>2048</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
Line 537: | Line 597: | ||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
<td>2040</td> | |||
</tr> | </tr> | ||
</table> | </table> |
Latest revision as of 10:48, 15 July 2020
Known switching classes of APN functions over GF(25), GF(26), GF(27) and GF(28).
Also available is Magma code generating representatives from the switching classes.
n | N | F(x) | Γ-rank | Δ-rank | Aut(dev(GF))/22n | Aut(dev(GF))/22n | Multiplier group |
---|---|---|---|---|---|---|---|
5 | 1.1 | x3 | 330 | 42 | 4960 | 4960 | 4960 |
1.2 | x5 | 330 | 42 | 4960 | 158720 | 4960 | |
2.1 | x-1 | 496 | 232 | 310 | 310 | 310 | |
6 | 1.1 | x3 | 1102 | 94 | 24192 | 48384 | 24192 |
1.2 | x3 + u11x6 + ux9 | 1146 | 94 | 4032 | 8064 | 4032 | |
2.1 | ux5 + x9 + u4x17 + ux18 + u4x20 + ux24 + u4x34 + ux40 | 1158 | 96 | 320 | 320 | 320 | |
2.2 | u7x3 + x5 + u3x9 + u4x10 + x17 + u6x18 | 1166 | 94 | 448 | 896 | 448 | |
2.3 | x3 + ux24 + x10 | 1166 | 96 | 896 | 896 | 896 | |
2.4 | x3 + u17(x17 + x18 + x20 + x24) | 1168 | 96 | 64 | 64 | 64 | |
2.5 | x3 + u11x5 + u13x9 + x17 + u11x33 + x48 | 1170 | 96 | 320 | 320 | 320 | |
2.6 | u25x5 + x9 + u38x12 + u25x18 + u25x36 | 1170 | 96 | 64 | 64 | 64 | |
2.7 | u40x5 + u10x6 + u62x20 + u35x33 + u15x34 + u29x48 | 1170 | 96 | 64 | 64 | 64 | |
2.8 | u34x6 + u52x9 + u48x12 + u6x20 + u9x33 + u23x34 + u25x40 | 1170 | 96 | 64 | 64 | 64 | |
2.9 | x9 + u4(x10 + x18) + u9(x12 + x20 + x40) | 1172 | 96 | 64 | 64 | 64 | |
2.10 | u52x3 + u47x5 + ux6 + u9x9 + u44x12 + u47x33 + u10x34 + u33x40 | 1172 | 96 | 64 | 64 | 64 | |
2.11 | u(x6 + x10 + x24 + x33) + x9 + u4x17 | 1174 | 96 | 64 | 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 | 8 | |
7 | 1.1 |
x3 |
3610 | 198 | 113792 | 113792 | 113792 |
1.2 |
x3 + Tr(x9) |
4026 | 212 | 896 | 896 | 896 | |
2.1 |
x34 + x18 + x5 |
4034 | 210 | 896 | 896 | 896 | |
2.2 |
x3 + x17 + x33 + x34 |
4040 | 212 | 896 | 896 | 896 | |
3.1 |
x5 |
3708 | 198 | 113792 | 113792 | 113792 | |
4.1 |
x9 |
3610 | 198 | 113792 | 14565376 | 113792 | |
5.1 |
x13 |
4270 | 338 | 889 | 889 | 889 | |
6.1 |
x57 |
4704 | 436 | 889 | 889 | 889 | |
7.1 |
x-1 |
8128 | 4928 | 1778 | 1778 | 1778 | |
8.1 |
x65 + x10 + x3 |
4038 | 212 | 896 | 896 | 896 | |
9.1 |
x3 + x9 + x18 + x66 |
4044 | 212 | 896 | 896 | 896 | |
10.1 |
x3 + x12 + x17 + x33 |
4048 | 210 | 896 | 896 | 896 | |
10.2 |
x3 + x17 + x20 + x34 + x66 |
4040 | 210 | 896 | 896 | 896 | |
11.1 |
x3 + x20 + x34 + x66 |
4048 | 210 | 896 | 896 | 896 | |
12.1 |
x3 + x12 + x40 + x72 |
4048 | 210 | 896 | 896 | 896 | |
13.1 |
x3 + x5 + x10 + x33 + x34 |
4040 | 212 | 896 | 896 | 896 | |
14.1 |
x3 + x6 + x34 + x40 + x72 |
4048 | 212 | 896 | 896 | 896 | |
14.2 |
x3 + x5 + x6 + x12 + x33 + x34 |
4050 | 210 | 896 | 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 | 128 | |
8 | 1.1 |
x3 |
11818 | 420 | 522240 | ||
1.2 |
x9 |
12370 | 420 | 522240 | |||
1.3 |
x3+Tr(x9) |
13800 | 432 | 6144 | |||
1.4 |
x9+Tr(x3) |
13804 | 434 | 6144 | |||
1.5 | x3+u245x33+u183x66+u21x144 | 13842 | 436 | 3072 | |||
1.6 | x3 + u65x18+u120x66+u135x144 | 13848 | 438 | 3072 | |||
1.7 | u188x192 + u129x144 + u172x132 + u138x129 + u74x96 + u244x72 + u22x66 + u178x48 + u150x36 + u146x33 + u6x24 + u60x18 + u80x12 + u140x9 + u221x6 + u19x3 | 14034 | 438 | 768 | |||
1.8 | u37x192 + u110x144 + u40x132 + u53x129 + u239x96 + u235x72 + u126x66 + u215x48 + u96x36 + u29x33 + u19x24 + u14x18 + u139x12 + u230x9 + u234x6 + u228x3 | 14032 | 438 | 3072 | |||
1.9 | u242x192 + u100x144 + u66x132 + u230x129 + u202x96 + u156x72 + u254x66 + u18x48 + u44x36 + u95x33 + u100x24 + u245x18 + u174x12 + u175x9 + u247x6 + u166x3 | 14036 | 438 | 3072 | |||
1.10 | u100x192 + u83x144 + u153x132 + u65x129 + u174x96 + u136x72 + u46x66+ u55x48+ u224x36+ u180x33+ u179x24+u226x18+ u54x12+ u168x9+ u89x6+ u56x3 | 14036 | 438 | 1536 | |||
1.11 | u77x192 + u133x144 + u47x132 + u229x129 + u23x96 + u242x72 + u242x66 + u245x48 + u212x36 + u231x33 + u174x24 + u216x18 + u96x12 + u253x9 + u154x6 + u71x3 | 14032 | 438 | 3072 | |||
1.12 | u220x192 + u94x144 + u70x132 + u159x129 + u145x96 + u160x72 + u74x66 + u184x48 + u119x36 + u106x33 + u253x24 + wx18 + u90x12 + u169x9 + u118x6 + u187x3 | 14034 | 438 | 3072 | |||
1.13 | u98x192 + u225x144 + u111x132 + u238x129 + u182x96 + u125x72 + u196x66 + u219x48 + u189x36 + u199x33 + u181x24 + u110x18 + u19x12 + u175x9 + u133x6 + u47x3 | 14030 | 438 | 1536 | |||
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 | 512 | |||
1.15 | u27x192 + u167x144 + u26x132 + u231x129 + u139x96 + u30x72 + u139x66 + u203x48 + u36x36 + u210x33 + u195x24 + u12x18 + u43x12 + u97x9 + u61x6 + u39x3 | 14036 | 454 | 768 | |||
1.16 | u6x192 + u85x144 + u251x132 + u215x129 + u229x96 + u195x72 + u152x66 + u173x48 + u209x36 + u165x33 + u213x24 + u214x18 + u158x12 + u146x9 + x6 + u50x3 | 14032 | 438 | 1536 | |||
1.17 | u164x192 + u224x144 + u59x132 + u124x129 + u207x96 + u211x72 + u5x66 + u26x48 + u20x36 + u101x33 + u175x24 + u241x18 + x12 + u15x9 + u217x6 + u212x3 | 14028 | 438 | 1536 | |||
2.1 | x3+ x17+u16(x18+x33)+u15x48 | 13200 | 414 | 46080 | |||
3.1 | x3+ u24x6+u182x132+u67x192 | 14024 | 438 | 3072 | |||
4.1 | x3+x6+x68+x80+x132+x160 | 14040 | 454 | 2048 | |||
5.1 | x3+x5+x18+x40+x66 | 14044 | 446 | 2048 | |||
6.1 | x3+x12+x40+x66+x130 | 14046 | 438 | 2048 | |||
7.1 |
x57 |
15358 | 960 | 2040 |