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0C1EF81D01F81E02F81E03F81804F81F0C158B8BFA7CFA7C058C0C1F8C0C221D 008C995C0C238C961D008C995C0EF77A0FF77D11F77B0C25F7830C2400060101 060E4E5C697F41646F62654964656E74697479436F7079726967687420323030 322041646F62652053797374656D7320496E636F72706F72617465642E20416C 6C205269676874732052657365727665642E2048696464656E20486F727A4F43 6C2F46535479706520382064656648696464656E486F727A4F436C2D44696E67 62617473000000000000010101020E0001010109F8200C269DF79012FB8E8B1C 05468B069F0A9F0B8C0C11FA7C14> endstr endstream endobj 62 0 obj <>stream q 403.1999969 0 0 336.9600067 0 239.0399933 cm /Im0 Do Q q 403.1999969 0 0 239.0399933 0 0 cm /Im1 Do Q BT /T1_0 1 Tf 0.05 Tc 3 Tr 10.1403 0 0 9 21.37 568.63 Tm (Proof: )Tj 9.349 0 0 9 64.18 568.63 Tm (The )Tj /C0_0 1 Tf 0 Tc 3.6541 0 0 6.6601 84.24 568.63 Tm <00650078002E0061006D0070006C0028007E00730020>Tj /T1_0 1 Tf 0.0495 Tc 9 0 0 9 125.37 568.63 Tm (constructed )Tj -0.0062 Tc 7.248 -0.02 Td (A. )Tj 0.0281 Tc 1.578 0 Td (Rosa )Tj -0.035 Tc 7.6372 0 0 9 228.78 568.45 Tm ([4] )Tj 0.05 Tc 9.2 0 0 9 276.49 568.45 Tm (both )Tj 0.0304 Tc 9 0 0 9 299.08 568.45 Tm (group )Tj 0.0411 Tc 3.06 0 Td (divisible )Tj 0.05 Tc 9.349 0 0 9 59.68 551.89 Tm (The )Tj 0.0148 Tc 9 0 0 9 21.33 534.96 Tm (class )Tj 0.0038 Tc 2.489 0 Td (will )Tj 0.0466 Tc 2.022 0 Td (be )Tj 0.0437 Tc 1.449 0 Td (our )Tj /C0_0 1 Tf 0 Tc 3.1321 0 0 6.8401 49.51 518.05 Tm <00610065004A006C00650074006C002E006E007E0020>Tj /T1_0 1 Tf 0.05 Tc 9.1661 0 0 9 84.76 518.05 Tm (this )Tj 0.0224 Tc 9 0 0 9 21.25 501.49 Tm (block )Tj 0.0044 Tc 2.704 0 Td (size )Tj 0 Tc 1.91 0 Td (4 )Tj 0.0256 Tc 0.843 0 Td (which )Tj 0.036 Tc 2.92 0 Td (has )Tj 0.05 Tc 9.5625 0 0 9 113.02 501.49 Tm (the )Tj 10.4588 0 0 9.1 21.33 472.15 Tm (Theorem )Tj 0 Tc 9.1 0 0 9.1 66.11 472.15 Tm (1 )Tj /T1_1 1 Tf 0.0311 Tc 8.7 0 0 8.7 77.22 472.15 Tm (There )Tj 0 Tc 8.8 0 0 8.8 21.19 455.05 Tm (n )Tj /T1_2 1 Tf 13.2 0 0 13.2 49.46 452.71 Tm (+ )Tj /T1_3 1 Tf 9.3 0 0 9.3 80.55 454.87 Tm (k )Tj /T1_2 1 Tf 13.6 0 0 13.6 116.42 452.53 Tm (+ )Tj /T1_3 1 Tf 0.0194 Tc 9.8 0 0 9.8 152.87 471.79 Tm (4,n\) )Tj /T1_1 1 Tf 0.05 Tc 8.8237 0 0 8.7 148.08 454.87 Tm (and )Tj 0 Tc 8.8 0 0 8.8 165.71 454.87 Tm (u )Tj /T1_2 1 Tf 13.2 0 0 13.2 174.02 454.87 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 9.2851 0 0 8.7 183.87 454.87 Tm (3k )Tj /T1_0 1 Tf 0.0404 Tc 9 0 0 9 213.39 518.23 Tm (on )Tj -0.035 Tc 8.942 0 0 9.1 227.29 518.23 Tm (24 )Tj 0.0106 Tc 9 0 0 9 238.85 551.71 Tm (which )Tj 0.0301 Tc 2.973 0 Td (is )Tj 0.0173 Tc 1.227 0 Td (halved: )Tj 0.05 Tc 9.0529 0 0 9 310.84 551.71 Tm (this )Tj 9.1782 0 0 9 329.77 551.71 Tm (parallel )Tj 0.0481 Tc 9 0 0 9 241.83 534.79 Tm (an )Tj 0.0437 Tc 1.462 0 Td (isomorphism )Tj 0.05 Tc 9.1801 0 0 9 309.95 534.79 Tm (with )Tj 0 Tc 9 0 0 9 331.65 534.79 Tm (a )Tj 0.027 Tc 0.979 0 Td (fixed )Tj 0.05 Tc 9.4612 0 0 9 268.37 518.05 Tm (with )Tj 0.0254 Tc 9 0 0 9 290.8 518.05 Tm (group )Tj 0.0178 Tc 2.954 0 Td (size )Tj 0 Tc 2.103 0 Td (3 )Tj 0.05 Tc 9.5174 0 0 9 345.32 518.05 Tm (and )Tj /T1_2 1 Tf 0 Tc 10.6 0 0 10.6 356.12 501.13 Tm (o )Tj /T1_0 1 Tf 8.6 0 0 8.6 208.86 455.05 Tm (1 )Tj /T1_1 1 Tf 0.05 Tc 9.0108 0 0 8.7 217.73 455.05 Tm (or )Tj /T1_0 1 Tf 0 Tc 8.6 0 0 8.6 229.64 455.05 Tm (4 )Tj /T1_1 1 Tf 0.05 Tc 8.8772 0 0 8.7 238.46 455.05 Tm (mod )Tj 0.036 Tc 8.7 0 0 8.7 320.7 471.79 Tm (all )Tj 0 Tc 1.451 0 Td (n)Tj 4.1 0 0 4.1 339.71 469.99 Tm (J )Tj 0.0378 Tc 9.9 0 0 9.9 346.48 471.79 Tm (\(A\) )Tj 0.05 Tc 8.8149 0 0 8.7 275.15 454.51 Tm (or )Tj 0.031 Tc 9.2 0 0 9.2 287.64 454.51 Tm (\(B\) )Tj 0 Tc 8.8 0 0 8.8 304.15 454.51 Tm (n )Tj /T1_2 1 Tf 8.7 0 0 8.7 313.96 454.51 Tm (= )Tj /T1_1 1 Tf 8.8 0 0 8.8 324.47 454.51 Tm (u )Tj /T1_2 1 Tf 12.6 0 0 12.6 332.79 454.51 Tm (+ )Tj /T1_1 1 Tf 0.0304 Tc 9.2 0 0 9.2 343.1 454.51 Tm (16k, )Tj 0 Tc 8.9 0 0 8.9 21.58 437.95 Tm (k )Tj /C0_0 1 Tf 5.9401 0 0 7.3801 29.52 437.95 Tm <007E0020>Tj /T1_1 1 Tf 0.0253 Tc 8.9 0 0 8.9 39.06 437.95 Tm (\(2u )Tj /T1_2 1 Tf 0 Tc 13.2 0 0 13.2 53.78 437.95 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 9.4872 0 0 9.1 62.49 437.95 Tm (1\)/4 )Tj /T1_1 1 Tf 8.8237 0 0 8.7 83.1 437.95 Tm (and )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 107.04 437.95 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 9.3714 0 0 8.9 115.3 437.95 Tm (4k )Tj /T1_0 1 Tf 0 Tc 9.1 0 0 9.1 137.93 437.95 Tm (1 )Tj /T1_1 1 Tf 0.05 Tc 8.8149 0 0 8.7 145.91 437.95 Tm (or )Tj /T1_0 1 Tf 0 Tc 9.1 0 0 9.1 156.56 437.95 Tm (4 )Tj /T1_1 1 Tf 0.05 Tc 9.1765 0 0 8.7 164.66 437.95 Tm (mod )Tj 0.0224 Tc 8.7 0 0 8.7 199.58 438.13 Tm (where )Tj 0 Tc 8.8 0 0 8.8 224.57 438.13 Tm (u )Tj /T1_0 1 Tf -0.035 Tc 8.8261 0 0 9.4 242.19 438.13 Tm (0, )Tj 0.05 Tc 9.3106 0 0 9.1 250.96 438.13 Tm (1,16,25 )Tj /T1_1 1 Tf 8.7106 0 0 8.7 286.14 438.13 Tm (and )Tj 8.887 0 0 8.7 317.84 437.77 Tm (with )Tj 0 Tc 8.9 0 0 8.9 338.02 437.77 Tm (k )Tj /T1_2 1 Tf -0.035 Tc 6.3758 0 0 12.1 345.76 437.77 Tm (1= )Tj 0 Tc 8.5 0 0 8.5 355.97 437.77 Tm (2 )Tj /T1_1 1 Tf 0.05 Tc 9.0108 0 0 8.7 21.89 421.21 Tm (or )Tj -0.035 Tc 8.1865 0 0 8.7 33.33 421.21 Tm (6. )Tj /T1_0 1 Tf 0.05 Tc 10.0086 0 0 9.1 21.38 394.57 Tm (Proof: )Tj 9.5625 0 0 9 88.9 394.57 Tm (the )Tj 0.0363 Tc 9 0 0 9 105.75 394.57 Tm (above )Tj 0.0474 Tc 2.98 0 Td (construction )Tj 0.05 Tc 9.4259 0 0 9 210.76 394.57 Tm (the )Tj 0.0117 Tc 9 0 0 9 227.14 394.57 Tm (two )Tj 0.0354 Tc 1.953 0 Td (group )Tj 0.0236 Tc 3.04 0 Td (divisible )Tj 0.05 Tc 9.2037 0 0 9 340.82 394.39 Tm (from )Tj 9.4259 0 0 9 21.22 377.83 Tm (the )Tj 0.0267 Tc 9 0 0 9 37.27 377.83 Tm (previous )Tj 0.0416 Tc 4.01 0 Td (lemma. )Tj 0 Tc 12.9 0 0 12.9 356.27 377.28 Tm (o )Tj 0.05 Tc 9.129 0 0 9 35.2 358.57 Tm (The )Tj 9.1783 0 0 9 92.14 358.57 Tm (table )Tj 0.046 Tc 9 0 0 9 115.25 358.57 Tm (summarizes )Tj 0.017 Tc 5.564 0 Td (all )Tj 0.05 Tc 9.4259 0 0 9 178 358.57 Tm (the )Tj 0.0239 Tc 9 0 0 9 194.02 358.57 Tm (various )Tj 0.0027 Tc 3.5 0 Td (values )Tj 0.0074 Tc 2.972 0 Td (of )Tj /T1_1 1 Tf 0.05 Tc 9.1621 0 0 8.8 262.72 358.57 Tm (u, )Tj 0 Tc 9.2 0 0 9.2 274.84 358.57 Tm (k )Tj /T1_0 1 Tf 0.05 Tc 9.1649 0 0 9 282.33 358.57 Tm (and )Tj /T1_1 1 Tf 0.0436 Tc 8.8 0 0 8.8 300.01 358.57 Tm (n. )Tj 0 Tc -20.252 -2.802 Td (u )Tj 9.2 0 0 9.2 139.12 333.91 Tm (k )Tj 8.8 0 0 8.8 171.67 333.73 Tm (n )Tj /T1_0 1 Tf 8.6 0 0 8.6 122.31 316.45 Tm (0 )Tj /T1_1 1 Tf 0.0267 Tc 9 0 0 9 138.7 316.27 Tm (3t )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 148.8 316.27 Tm (+ )Tj /T1_2 1 Tf 8.5 0 0 8.5 157.77 316.27 Tm (1 )Tj /T1_1 1 Tf 0.0382 Tc 9 0 0 9 171.64 316.45 Tm (48t )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 186.96 316.45 Tm (+ )Tj 0.0133 Tc 8.6 0 0 8.6 196.08 316.45 Tm (16 )Tj 0 Tc 9.1 0 0 9.1 230.31 316.63 Tm (0 )Tj /T1_2 1 Tf 8.5 0 0 8.5 122.49 299.71 Tm (1 )Tj /T1_1 1 Tf 0.0164 Tc 9 0 0 9 138.52 299.89 Tm (4t )Tj 0.0172 Tc 3.701 0 Td (96t )Tj /T1_0 1 Tf 0 Tc 9.1 0 0 9.1 196.07 299.89 Tm (1 )Tj /T1_1 1 Tf 10 0 0 10 214.26 299.89 Tm (t )Tj /T1_0 1 Tf 8.6 0 0 8.6 230.31 299.71 Tm (0 )Tj 9.1 0 0 9.1 122.63 283.15 Tm (1 )Tj /T1_1 1 Tf 0.0164 Tc 9 0 0 9 138.7 282.97 Tm (4t )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 148.8 282.97 Tm (+ )Tj 8.8 0 0 8.8 157.74 282.97 Tm (1 )Tj /T1_1 1 Tf 0.0172 Tc 9 0 0 9 172.01 282.97 Tm (96t )Tj /T1_0 1 Tf 0 Tc 11 0 0 11 186.79 282.97 Tm (+ )Tj -0.035 Tc 8.942 0 0 9.1 195.97 282.97 Tm (25 )Tj /T1_1 1 Tf 0 Tc 9 0 0 9 214.45 283.15 Tm (t )Tj /T1_0 1 Tf 9.1 0 0 9.1 230.49 283.15 Tm (0 )Tj -11.873 -1.859 Td (1 )Tj /T1_1 1 Tf 0.0267 Tc 9 0 0 9 138.7 266.41 Tm (3t )Tj 0.0382 Tc 3.66 -0.04 Td (48t )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 186.96 266.05 Tm (+ )Tj 8.6 0 0 8.6 196.08 266.05 Tm (1 )Tj -0.035 Tc 9.0505 0 0 9.1 230.17 265.87 Tm (2, )Tj /T1_1 1 Tf 0 Tc 9 0 0 9 240.01 265.87 Tm (t )Tj /C0_0 1 Tf 5.9401 0 0 6.8401 246.25 265.87 Tm <007E0020>Tj /T1_2 1 Tf 8.5 0 0 8.5 255.86 265.87 Tm (0 )Tj /T1_0 1 Tf 0.0133 Tc 8.6 0 0 8.6 120.3 249.31 Tm (16 )Tj /T1_1 1 Tf 0.0164 Tc 9 0 0 9 138.7 249.49 Tm (4t )Tj 0.0272 Tc 3.701 -0.04 Td (96t )Tj /T1_0 1 Tf 0 Tc 11 0 0 11 187.15 249.13 Tm (+ )Tj -0.0077 Tc 8.6 0 0 8.6 196.26 249.13 Tm (16 )Tj 0 Tc 9 0 0 9 230.48 249.31 Tm (3 )Tj -0.035 Tc 8.8631 0 0 9.1 120.47 232.57 Tm (16 )Tj /T1_1 1 Tf 0.0364 Tc 9 0 0 9 138.7 232.21 Tm (4t )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 148.98 232.21 Tm (+ )Tj 9 0 0 9 157.76 232.21 Tm (3 )Tj /T1_1 1 Tf 0.0272 Tc 1.583 0 Td (96t )Tj /T1_0 1 Tf 0 Tc 11 0 0 11 186.97 232.21 Tm (+ )Tj -0.0346 Tc 8.9 0 0 8.9 196.04 232.21 Tm (88 )Tj 0 Tc 9.1 0 0 9.1 230.71 232.57 Tm (2 )Tj 0.0199 Tc 8.6 0 0 8.6 120.02 215.29 Tm (40 )Tj /T1_1 1 Tf 0.0364 Tc 9 0 0 9 138.7 215.47 Tm (4t )Tj 0.0272 Tc 3.701 -0.04 Td (96t )Tj /T1_0 1 Tf 0 Tc 11 0 0 11 186.97 215.11 Tm (+ )Tj -0.035 Tc 9.0976 0 0 9.1 195.98 215.11 Tm (40 )Tj /C0_0 1 Tf 0 Tc 6.6601 0 0 7.0201 214.75 214.93 Tm <0074007E00370020>Tj /T1_0 1 Tf -0.035 Tc 8.7518 0 0 9.1 120.37 198.37 Tm (25 )Tj /T1_1 1 Tf 9.7731 0 0 10.1 138.87 198.37 Tm (3t )Tj 0.0382 Tc 9 0 0 9 172 198.19 Tm (48t )Tj /T1_0 1 Tf 0 Tc 11 0 0 11 187.15 198.19 Tm (+ )Tj -0.035 Tc 8.7518 0 0 9.1 196.33 198.19 Tm (25 )Tj /C0_0 1 Tf 0 Tc 6.5401 0 0 7.0201 214.93 197.83 Tm <0074007E00350020>Tj /T1_0 1 Tf 0.05 Tc 9.0045 0 0 9 21.56 175.87 Tm (From )Tj 9.2893 0 0 9 45.52 175.87 Tm (the )Tj 0.0263 Tc 9 0 0 9 61.29 175.87 Tm (above )Tj 0.05 Tc 9.1783 0 0 9 87.1 175.87 Tm (table )Tj -0.0206 Tc 9 0 0 9 110.15 175.87 Tm (we )Tj 0.0051 Tc 1.527 0 Td (see )Tj 0.05 Tc 9.4124 0 0 9 138.94 175.87 Tm (that )Tj -0.0206 Tc 9 0 0 9 158.39 175.87 Tm (we )Tj 0.05 Tc 9.083 0 0 9 172.17 175.87 Tm (are )Tj 0.0326 Tc 9 0 0 9 187.54 175.87 Tm (missing )Tj 0.0278 Tc 3.652 0 Td [(only )-62(nine )]TJ 0.0399 Tc 4.42 0 Td (admissible )Tj 0.0321 Tc 4.92 0 Td (orders. )Tj /T1_1 1 Tf 0 Tc 8.7 0 0 8.7 68.79 151.39 Tm (1 )Tj 0.0311 Tc 1.217 0 Td (There )Tj 0.0391 Tc 2.991 0 Td (exists )Tj 0 Tc 2.899 0 Td (a )Tj /T1_0 1 Tf 0.05 Tc 9.2613 0 0 9.1 166.75 151.57 Tm (3\(2,4, )Tj /T1_1 1 Tf 9.761 0 0 8.7 192.73 151.57 Tm (n\) )Tj 0.0427 Tc 8.7 0 0 8.7 206.06 151.57 Tm (with )Tj 0.0241 Tc 2.31 0 Td (the )Tj 0.024 Tc 1.744 0 Td (halving )Tj /T1_3 1 Tf 0.05 Tc 4.8246 0 0 3.7001 272.88 151.57 Tm ('l'lTIH'lP'Y't11 )Tj /T1_1 1 Tf 8.8925 0 0 8.7 308.09 151.57 Tm (for )Tj 0.0257 Tc 8.7 0 0 8.7 323.58 151.57 Tm (all )Tj 0 Tc 1.471 0 Td (n )Tj /T1_2 1 Tf -0.035 Tc 6.0689 0 0 11.8 345.68 151.57 Tm (== )Tj 0 Tc 8.5 0 0 8.5 356.49 151.57 Tm (1 )Tj /T1_1 1 Tf 0.05 Tc 9.0108 0 0 8.7 22.07 134.28 Tm (or )Tj /T1_0 1 Tf -0.035 Tc 8.6617 0 0 9.1 34.08 134.28 Tm (16 )Tj /T1_1 1 Tf 0.05 Tc 9.0767 0 0 8.7 47.12 134.28 Tm (mod )Tj /T1_0 1 Tf -0.035 Tc 8.942 0 0 9.1 66.91 134.28 Tm (24 )Tj /T1_1 1 Tf 0.0427 Tc 8.7 0 0 8.7 80.24 134.28 Tm (with )Tj 0.0241 Tc 2.331 0 Td (the )Tj 0.0192 Tc 1.783 0 Td (possible )Tj 0.0407 Tc 3.971 0 Td (exception )Tj 0.05 Tc 10.2615 0 0 8.7 191.07 134.28 Tm (of )Tj 0 Tc 8.7 0 0 8.7 201.74 134.28 Tm (n )Tj /T1_2 1 Tf 8.1 0 0 8.1 211.01 134.28 Tm (= )Tj /T1_0 1 Tf -0.0057 Tc 8.6 0 0 8.6 221.85 134.28 Tm (73, )Tj -0.0255 Tc 9.1 0 0 9.1 236.57 134.28 Tm (169, )Tj -0.0319 Tc 2.097 0 Td (184 )Tj /T1_1 1 Tf 0.05 Tc 8.7106 0 0 8.7 274.08 134.28 Tm (and )Tj 0 Tc 8.7 0 0 8.7 291.38 134.28 Tm (n )Tj /T1_0 1 Tf 10.5 0 0 10.5 300.73 134.28 Tm (= )Tj /T1_1 1 Tf 0.0189 Tc 8.7 0 0 8.7 310.97 134.28 Tm (96t )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 326.1 134.28 Tm (+ )Tj 0.0409 Tc 8.6 0 0 8.6 335.3 134.28 Tm (40 )Tj /T1_1 1 Tf 0.05 Tc 9.4156 0 0 8.7 348.8 134.28 Tm (for )Tj 12.0228 0 0 9.4 21.28 117.18 Tm (t=1,2, )Tj 11.8554 0 0 9.4 56.41 117.18 Tm (... )Tj 9.4392 0 0 9.4 68.79 117.18 Tm (,6. )Tj /T1_0 1 Tf 10.3962 0 0 9.1 21.72 90.36 Tm (Lemma )Tj 0 Tc 9.1 0 0 9.1 59.17 90.36 Tm (2 )Tj /T1_1 1 Tf 0.0259 Tc 8.7 0 0 8.7 70.2 90.36 Tm (There )Tj 0.0391 Tc 2.929 0 Td (exists )Tj 0 Tc 2.878 0 Td (a )Tj 0.0211 Tc 0.913 0 Td (design )Tj /T1_0 1 Tf 0.05 Tc 9.332 0 0 9.1 155.95 90.36 Tm (3\(2,4, )Tj /T1_1 1 Tf 9.761 0 0 8.7 181.93 90.36 Tm (n\) )Tj 8.7904 0 0 8.7 195.08 90.36 Tm (with )Tj 0.0344 Tc 8.7 0 0 8.7 215 90.36 Tm (the )Tj 0.024 Tc 1.723 0 Td (halving )Tj 0.0487 Tc 3.536 0 Td (property )Tj 0.05 Tc 8.8925 0 0 8.7 296.21 90.36 Tm (for )Tj 0 Tc 8.7 0 0 8.7 310.46 90.36 Tm (n )Tj /T1_0 1 Tf 11.9 0 0 11.9 318.9 90.36 Tm (= )Tj -0.0193 Tc 9.1 0 0 9.1 328.76 90.36 Tm (73, )Tj 0.0405 Tc 8.6 0 0 8.6 344.04 90.36 Tm (169, )Tj -0.0247 Tc 9.1 0 0 9.1 21.83 73.09 Tm (520. )Tj 0.0146 Tc 8.7 0 0 8.7 181.21 48.07 Tm (233 )Tj ET endstream endobj 68 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 50215/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream TN̏ÝXdte5B"!Fv$莈.#tGG]#,DtEL#&9C""&Z;&4]C!fBDJ|">eX-#%XDqY'*09C`,t)&H躄c0uH$>q!G1a8BP&e -HjlY.v \#Ǒ& ;Gv!0pEnlB# ]Lt6.q#J@*!pD}ߖ< F c#BG\cIcL͑WIOPDt#/v#`LR0ꛥ֓YiG++KGDtmDtjDt]vmҫGpD}#toQL":q= BdtK:#>HPڊmc#:z "?t,Jru+ڮ#Q2=0!h1h㕉,RI.f":.H:%(蜈莎":#DtGDtjE:6y]QGTm(FN@0C#GGZ\f":@:E">QDu‹."Dy#:B vH2>G(r! !Gi@!DtatH*9T9TW0tF"!+D|hz-{ڈL@Xql @aG$ :L&G9(p@A DtcBN-:D4Ipg IHEA!H#BG!G.HDtJH"?BXv8"?F.dt #D'} @!,8 0 yXAD 莐IFC#t9CA!& :EyI(!@8A C„Gq HA:#2($}DHJ(":AoGރ!NaGD~CGňQJDt,S(c GaHD9H!aH$ бYCJP(c`$Z M*҃ >GW !hDF4U  I$")='@I䁂\ir>GTFm93ZiVdt"E 7T#D~.!JGL!6: ":#A(0Dt:A4b(T,D1aІ.AÄ ZA#RI<2:#EP"N°@B#>a !4# !a$!5":#t!莉ѭn!HyDnu(tdtAYӨqZqI$׸ GMj-:JA LlR EBA:I_(q)0& E= CpD}8pDx!i!q(vC HLÓL 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9.2893 0 0 9 138.76 528.49 Tm (the )Tj 0.0345 Tc 9 0 0 9 154.18 528.49 Tm (groups )Tj /T1_1 1 Tf 0 Tc 3.3 0 Td (G )Tj /T1_0 1 Tf 0.044 Tc 1.099 0 Td (and )Tj 0.05 Tc 9.2893 0 0 9 210.94 528.49 Tm (the )Tj 0.0281 Tc 9 0 0 9 226.27 528.49 Tm (blocks )Tj /T1_1 1 Tf 0 Tc 3.107 0 Td (B )Tj /T1_0 1 Tf 0.05 Tc 9.8699 0 0 9 264.32 528.49 Tm (and )Tj 0 Tc 9 0 0 9 283.05 528.49 Tm (a )Tj 0.05 Tc 9.5112 0 0 9 290.35 528.49 Tm (permutation )Tj 6.4813 0 0 5.8001 343.91 528.49 Tm (0: )Tj 0.0274 Tc 9 0 0 9 352.35 528.49 Tm (of )Tj /T1_1 1 Tf 0 Tc 1.153 0 Td (V )Tj /T1_0 1 Tf 0.05 Tc 9.1127 0 0 9 26.98 511.75 Tm (mapping )Tj 9.8357 0 0 9 64.24 511.75 Tm (the )Tj 9.0691 0 0 9 80.02 511.75 Tm (groups )Tj 9.2824 0 0 9 110.25 511.75 Tm (and )Tj 0.0201 Tc 9 0 0 9 127.81 511.75 Tm (blocks )Tj 0.0391 Tc 3.031 0 Td (in )Tj 0.0287 Tc 1.098 0 Td (one )Tj 0.05 Tc 9.3507 0 0 9 181.45 511.75 Tm (part )Tj 0.0453 Tc 9 0 0 9 200.5 511.75 Tm (to )Tj 0.0333 Tc 1.14 0 Td (those )Tj 0.05 Tc 9.1016 0 0 9 233.93 511.75 Tm (in )Tj 9.4259 0 0 9 244.06 511.75 Tm (the )Tj 9.6749 0 0 9 259.29 511.75 Tm (other )Tj 9.4785 0 0 9 283.69 511.75 Tm (part. )Tj 0.0207 Tc 9 0 0 9 307.77 511.75 Tm (We )Tj 0.05 Tc 9.1116 0 0 9 323.19 511.75 Tm (denote )Tj 0.0311 Tc 9 0 0 9 352.31 511.75 Tm (such )Tj 0 Tc -36.136 -1.88 Td (a )Tj 0.05 Tc 9.2981 0 0 9 34.93 494.83 Tm (partition )Tj 9.5157 0 0 9 73.63 494.83 Tm (by )Tj /T1_2 1 Tf 0 Tc 9.4 0 0 9.4 87.47 494.83 Tm (G )Tj /T1_3 1 Tf 8.7 0 0 8.7 97.42 494.83 Tm (= )Tj /T1_2 1 Tf 0.0041 Tc 9.4 0 0 9.4 107.45 494.83 Tm (G' )Tj /T1_3 1 Tf 0 Tc 11.2 0 0 11.2 119.13 494.83 Tm (u )Tj /C0_0 1 Tf 5.3101 0 0 7.0201 127.99 494.83 Tm <0047007E0020>Tj /T1_0 1 Tf 0.05 Tc 9.2824 0 0 9 142.83 494.83 Tm (and )Tj /T1_2 1 Tf 0 Tc 9.4 0 0 9.4 160.99 494.83 Tm (B )Tj 0.05 Tc 10.3021 0 0 9.4 180.98 494.83 Tm (B' )Tj /T1_3 1 Tf 0 Tc 7.8001 0 0 7.8001 192.6 494.83 Tm (U )Tj /C0_0 1 Tf 5.2201 0 0 7.0201 200.71 494.83 Tm <0042007E0020>Tj /T1_0 1 Tf 0.0309 Tc 9 0 0 9 214.91 494.83 Tm (where )Tj 0.05 Tc 6.7048 0 0 5.8001 241.49 494.83 Tm (0: )Tj 0 Tc 5.8001 0 0 5.8001 250.6 494.83 Tm (: )Tj /T1_2 1 Tf 0.05 Tc 10.0961 0 0 9.4 255.67 494.83 Tm (B' )Tj /T1_3 1 Tf 9.6867 0 0 7.4001 267.75 494.83 Tm (-+ )Tj /T1_0 1 Tf 9.5174 0 0 9 295.64 494.83 Tm (and )Tj 6.7048 0 0 5.8001 314.21 494.83 Tm (0: )Tj 0 Tc 5.8001 0 0 5.8001 322.96 494.83 Tm (: )Tj /T1_2 1 Tf 9.4 0 0 9.4 328.13 494.83 Tm (G)Tj /T1_1 1 Tf 4.4001 0 0 4.4001 334.97 498.4299 Tm (1 )Tj /C0_0 1 Tf 8.2801 0 0 7.0201 340.57 494.83 Tm <007E0020>Tj 4.5001 0 0 7.0201 352.45 494.83 Tm <0047007E002E0020>Tj /T1_0 1 Tf 0.0492 Tc 9 0 0 9 40.84 477.91 Tm (Assume )Tj 0.05 Tc 10.2879 0 0 9 74.67 477.91 Tm (that )Tj 9.3543 0 0 9 94.66 477.91 Tm (there )Tj 0.045 Tc 9 0 0 9 117.8 477.91 Tm (exists )Tj 0.05 Tc 9.1655 0 0 9 142.83 477.91 Tm (an )Tj /T1_2 1 Tf 0.0078 Tc 9.7 0 0 9.7 155.15 477.91 Tm (S\(2,4,u\), )Tj -0.035 Tc 8.9495 0 0 9.7 191.88 477.91 Tm (\(U, )Tj 0 Tc 9.7 0 0 9.7 205.81 477.91 Tm (B)Tj /T1_1 1 Tf 4.9001 0 0 4.9001 212.13 476.6499 Tm (u)Tj 0.05 Tc 7.3772 0 0 4.9001 217.02 477.91 Tm (\), )Tj /T1_0 1 Tf 0.0356 Tc 9 0 0 9 224.81 477.91 Tm (which )Tj 0.026 Tc 2.88 0 Td (has )Tj 0.05 Tc 10.3822 0 0 9 266.01 477.91 Tm (the )Tj 9.0736 0 0 9 282.23 477.91 Tm (halving )Tj 9.2246 0 0 9 315.01 477.91 Tm (property )Tj 0.0495 Tc 9 0 0 9 352.07 477.91 Tm (with )Tj 0.05 Tc 9.4259 0 0 9 26.8 460.99 Tm (the )Tj 9.1849 0 0 9 43.12 460.99 Tm (isomorphism )Tj -0.035 Tc 5.1142 0 0 5.8001 99.13 460.99 Tm (0:1.4 )Tj 0.05 Tc 9.5174 0 0 9 113.12 460.99 Tm (and )Tj 0 Tc 9 0 0 9 132.03 460.99 Tm (a )Tj 0.0475 Tc 0.908 0 Td (transversal )Tj 0.05 Tc 9.1619 0 0 9 215.74 460.99 Tm (TD\( )Tj /T1_2 1 Tf 0.0013 Tc 9.7 0 0 9.7 233.08 460.99 Tm (k,4\) )Tj /T1_0 1 Tf 0.033 Tc 9 0 0 9 252.61 460.99 Tm (\(on )Tj /T1_2 1 Tf 0.05 Tc 10.4739 0 0 9.7 269.19 460.99 Tm (4k )Tj /T1_0 1 Tf 9.1086 0 0 9 283.69 460.99 Tm (points, )Tj /T1_2 1 Tf -0.035 Tc 8.3229 0 0 9.7 316.09 460.99 Tm (Z4 )Tj /T1_0 1 Tf 0 Tc 9 0 0 9 329.19 460.99 Tm (x )Tj 0.0495 Tc 2.542 0 Td (with )Tj 0.0265 Tc -36.128 -1.86 Td (groups )Tj 0.0274 Tc 3.239 0 Td (of )Tj 0.05 Tc 10.1045 0 0 9 66.64 444.25 Tm (sizek )Tj 9.3999 0 0 9 92.6 444.25 Tm (and )Tj 0.0321 Tc 9 0 0 9 110.53 444.25 Tm (blocks )Tj 0.0074 Tc 3.109 0 Td (of )Tj 0.0111 Tc 1.116 0 Td (size )Tj 0.0023 Tc 1.89 0 Td (4\) )Tj -0.0282 Tc 10.1 0 0 10.1 176.82 444.25 Tm (\(cf )Tj -0.035 Tc 8.9223 0 0 9 190.23 444.25 Tm ([1]\). )Tj 0.0233 Tc 9 0 0 9 209.43 444.25 Tm (Given )Tj 0 Tc 2.86 0 Td (a )Tj 0.0354 Tc 0.821 0 Td (group )Tj 0.05 Tc 9.0212 0 0 9 268.3 444.25 Tm (divisible )Tj 0.032 Tc 9 0 0 9 305.92 444.25 Tm (design )Tj /T1_1 1 Tf -0.035 Tc 9.263 0 0 9.4 334.03 444.25 Tm (\(V, )Tj 0.05 Tc 9.726 0 0 9.4 358.98 444.25 Tm (B\) )Tj /T1_0 1 Tf 0.0428 Tc 9 0 0 9 26.99 427.33 Tm (with )Tj 0.05 Tc 9.5625 0 0 9 48.04 427.33 Tm (the )Tj 9.2375 0 0 9 64.61 427.33 Tm (halving )Tj 9.3695 0 0 9 99.19 427.33 Tm (property )Tj 9.1649 0 0 9 137.97 427.33 Tm (and )Tj 0.0397 Tc 9 0 0 9 156.35 427.33 Tm (isomorphism )Tj -0.035 Tc 7.8897 0 0 10 210.34 427.33 Tm (0:, )Tj 8.9557 0 0 9 222.11 427.33 Tm (we )Tj 0.05 Tc 9.1293 0 0 9 235.89 427.33 Tm (construct )Tj 0 Tc 9 0 0 9 277.83 427.33 Tm (a )Tj 0.044 Tc 0.921 0 Td (design )Tj /T1_2 1 Tf 0.0078 Tc 9.7 0 0 9.7 316.07 427.33 Tm (S\(2,4,n\), )Tj 0 Tc 3.911 0 Td (n )Tj /T1_1 1 Tf 8.1 0 0 8.1 363.03 427.33 Tm (= )Tj /T1_2 1 Tf 9.4 0 0 9.4 26.74 410.59 Tm (u )Tj /T1_0 1 Tf 11.9 0 0 11.9 34.68 410.59 Tm (+ )Tj /T1_2 1 Tf 0.05 Tc 10.2675 0 0 9.4 43.14 410.59 Tm (vk )Tj /T1_0 1 Tf 9.0909 0 0 9 56.07 410.59 Tm (on )Tj 9.9723 0 0 9 69.46 410.59 Tm (the )Tj 0.0481 Tc 9 0 0 9 86.45 410.59 Tm (set )Tj /T1_2 1 Tf 0 Tc 9.4 0 0 9.4 101.22 410.59 Tm (U )Tj /T1_0 1 Tf 9 0 0 9 111.05 410.59 Tm (U )Tj /T1_2 1 Tf 9.4 0 0 9.4 119.35 410.59 Tm (V )Tj /T1_0 1 Tf 9 0 0 9 130.11 410.59 Tm (x )Tj /T1_2 1 Tf 9.4 0 0 9.4 138.86 410.59 Tm (K )Tj /T1_0 1 Tf 0.0306 Tc 9 0 0 9 150.11 410.59 Tm (which )Tj 0.0105 Tc 2.94 0 Td (will )Tj 0.0193 Tc 1.94 0 Td (have )Tj 0.05 Tc 9.2893 0 0 9 214.9 410.59 Tm (the )Tj 0.0412 Tc 9 0 0 9 230.57 410.59 Tm (halving )Tj 0.05 Tc 9.5144 0 0 9 263.17 410.59 Tm (property )Tj 0.0391 Tc 9 0 0 9 302.31 410.59 Tm (as )Tj -0.0077 Tc 1.279 0 Td (follows: )Tj 0.0065 Tc -30.321 -1.88 Td (\(1\) )Tj 0.0174 Tc 1.661 0 Td (for )Tj 0.05 Tc 9.371 0 0 9 71.36 393.67 Tm (each )Tj /T1_2 1 Tf 0 Tc 9.7 0 0 9.7 94.43 393.67 Tm (b )Tj /T1_0 1 Tf 8.1 0 0 8.1 102.38 393.67 Tm (E )Tj /T1_2 1 Tf 0.05 Tc 10.5082 0 0 9.7 112.4 393.67 Tm (B' )Tj /T1_0 1 Tf 9.1459 0 0 9 125.8 393.67 Tm (take )Tj 9.4259 0 0 9 146.86 393.67 Tm (the )Tj 0.0241 Tc 9 0 0 9 163.27 393.67 Tm (blocks )Tj 0.0074 Tc 3.189 0 Td (of )Tj 0 Tc 1.22 0 Td (a )Tj 0.05 Tc 9.1619 0 0 9 211.06 393.67 Tm (TD\( )Tj /T1_2 1 Tf -0.0048 Tc 9.7 0 0 9.7 228.4 393.67 Tm (k,4\) )Tj /T1_0 1 Tf 0.05 Tc 9.2745 0 0 9 247.95 393.67 Tm (constructed )Tj 9.2658 0 0 9 299.43 393.67 Tm (on )Tj 9.4259 0 0 9 313.54 393.67 Tm (the )Tj 0.0381 Tc 9 0 0 9 330.35 393.67 Tm (set )Tj /T1_2 1 Tf 0 Tc 9.7 0 0 9.7 345.89 393.67 Tm (b )Tj /T1_0 1 Tf 9 0 0 9 352.95 393.67 Tm (x )Tj /T1_2 1 Tf 9.7 0 0 9.7 362.06 393.67 Tm (K )Tj /T1_0 1 Tf 0.0309 Tc 9 0 0 9 26.81 376.9299 Tm (where )Tj 0.05 Tc 9.5625 0 0 9 53.44 376.9299 Tm (the )Tj 9.1909 0 0 9 69.58 376.9299 Tm (groups )Tj 9.083 0 0 9 100.71 376.9299 Tm (are )Tj 9.6991 0 0 9 116.62 376.9299 Tm (the )Tj 0.0291 Tc 9 0 0 9 132.89 376.9299 Tm (sets )Tj /T1_2 1 Tf 0.0274 Tc 9.7 0 0 9.7 151 376.9299 Tm ({a} )Tj /T1_0 1 Tf 0.0303 Tc 9 0 0 9 201.32 376.9299 Tm (each )Tj /T1_2 1 Tf 0 Tc 9.7 0 0 9.7 222.06 376.9299 Tm (a )Tj /T1_0 1 Tf 8.1 0 0 8.1 229.82 376.9299 Tm (E )Tj /T1_1 1 Tf -0.035 Tc 7.1703 0 0 9 238.43 376.9299 Tm (h; )Tj /T1_0 1 Tf 0.0065 Tc 9 0 0 9 40.93 359.83 Tm (\(2\) )Tj 0.0174 Tc 1.641 0 Td (for )Tj 0.05 Tc 9.371 0 0 9 71 359.83 Tm (each )Tj /T1_2 1 Tf 0 Tc 8.8 0 0 8.8 93.32 359.83 Tm (g )Tj /T1_3 1 Tf 7.8001 0 0 7.8001 102.24 359.83 Tm (E )Tj /T1_2 1 Tf 0.0344 Tc 9.1 0 0 9.1 112.14 359.83 Tm (G' )Tj /T1_0 1 Tf 0.05 Tc 9.1459 0 0 9 125.26 359.83 Tm (take )Tj 9.4259 0 0 9 145.96 359.83 Tm (the )Tj 0.0241 Tc 9 0 0 9 162.55 359.83 Tm (blocks )Tj 0.0274 Tc 3.129 0 Td (of )Tj 0 Tc 1.24 0 Td (a )Tj 0.05 Tc 9.2745 0 0 9 277.65 359.83 Tm (constructed )Tj 0.0404 Tc 9 0 0 9 328.95 359.83 Tm (on )Tj 0.05 Tc 9.4259 0 0 9 342.34 359.83 Tm (the )Tj 0.0281 Tc 9 0 0 9 358.79 359.83 Tm (set )Tj /T1_2 1 Tf 0 Tc 9.7 0 0 9.7 27.06 342.91 Tm (U )Tj /T1_3 1 Tf 10.8 0 0 10.8 36.52 342.91 Tm (u )Tj /T1_0 1 Tf 9 0 0 9 52.53 342.91 Tm (x )Tj 0.05 Tc 9.1029 0 0 9 75.59 342.91 Tm (having )Tj 9.5625 0 0 9 106.54 342.91 Tm (the )Tj /T1_2 1 Tf -0.035 Tc 9.2382 0 0 9.7 165.42 342.91 Tm (\(U, )Tj -0.0078 Tc 9.7 0 0 9.7 179.71 342.91 Tm (Bu\), )Tj /T1_0 1 Tf 0.0209 Tc 9 0 0 9 199.61 342.91 Tm (where )Tj 0 Tc 2.899 0 Td (m )Tj /T1_2 1 Tf 8.8 0 0 8.8 246.17 342.91 Tm (u )Tj /T1_3 1 Tf 13.6 0 0 13.6 253.58 342.91 Tm (+ )Tj -0.035 Tc 8.7083 0 0 12.7 263.46 342.91 Tm (Igi )Tj /T1_2 1 Tf 0.002 Tc 9.7 0 0 9.7 275.38 342.91 Tm (k. )Tj /T1_0 1 Tf 0.05 Tc 9.349 0 0 9 40.78 326.35 Tm (The )Tj 9.0876 0 0 9 59.67 326.35 Tm (above )Tj 0.0359 Tc 9 0 0 9 87.21 326.35 Tm (collection )Tj 0.0274 Tc 4.62 0 Td (of )Tj 0.0251 Tc 1.191 0 Td (blocks, )Tj 0.0443 Tc 3.41 0 Td (denoted )Tj 0.0096 Tc 3.85 0 Td (by )Tj /T1_2 1 Tf 0.028 Tc 9.4 0 0 9.4 217.53 326.35 Tm (D', )Tj /T1_0 1 Tf 0.0171 Tc 9 0 0 9 232.91 326.35 Tm (will )Tj 0.0259 Tc 1.93 0 Td (form )Tj 0.05 Tc 9.6404 0 0 9 272.15 326.35 Tm (half )Tj 9.1816 0 0 9 291.33 326.35 Tm (of )Tj 9.8357 0 0 9 302.38 326.35 Tm (the )Tj 0.0241 Tc 9 0 0 9 318.97 326.35 Tm (blocks )Tj 0.0274 Tc 3.089 0 Td (of )Tj 0.05 Tc 9.1527 0 0 9 357.46 326.35 Tm (the )Tj 0.0275 Tc 9 0 0 9 27.56 309.4299 Tm (S\(2,4,n\) )Tj 0.0407 Tc 7.434 0 Td (We )Tj 0.0226 Tc 1.794 0 Td (define )Tj 0.05 Tc 9.2893 0 0 9 137.14 309.4299 Tm (the )Tj 9.2404 0 0 9 152.65 309.4299 Tm (permutation )Tj 7.1277 0 0 5.8001 204.59 309.4299 Tm (0:' )Tj 0.0296 Tc 9 0 0 9 215.29 309.4299 Tm (by )Tj /T1_2 1 Tf -0.0244 Tc 9.7 0 0 9.7 227.44 309.4299 Tm (o:'\(x,)Tj /T1_0 1 Tf 0.0449 Tc 9.3 0 0 9.3 248.5 309.4299 Tm (i\) )Tj /T1_2 1 Tf 0.05 Tc 10.5247 0 0 9.7 267.63 309.4299 Tm (\(a\(x\),i\) )Tj /T1_0 1 Tf 0.0274 Tc 9 0 0 9 304.28 309.4299 Tm (for )Tj /T1_2 1 Tf 0 Tc 9.7 0 0 9.7 319.07 309.4299 Tm (x )Tj /T1_0 1 Tf 8.7 0 0 8.7 326.83 309.4299 Tm (E )Tj /T1_1 1 Tf -0.035 Tc 8.2205 0 0 9 335.58 309.4299 Tm (V, )Tj /T1_0 1 Tf 0 Tc 9.3 0 0 9.3 347.14 309.4299 Tm (i )Tj 8.7 0 0 8.7 353.29 309.4299 Tm (E )Tj /T1_1 1 Tf 9 0 0 9 361.87 309.4299 Tm (K )Tj /T1_0 1 Tf 0.044 Tc -37.158 -1.88 Td (and )Tj 0.0226 Tc 2.001 0 Td (define )Tj -0.0315 Tc 10 0 0 10 73.16 292.5099 Tm (0:'\(5\) )Tj -0.035 Tc 7.5636 0 0 10 108.64 292.5099 Tm (0:1.4\(8\), )Tj /T1_1 1 Tf 8.1951 0 0 8.9 154.75 292.5099 Tm (U, )Tj /T1_0 1 Tf 0.0309 Tc 9 0 0 9 167.39 292.5099 Tm (where )Tj -0.035 Tc 6.7463 0 0 10 194.69 292.5099 Tm (0: )Tj 0.05 Tc 9.0474 0 0 9 203.85 292.5099 Tm (and )Tj /T1_3 1 Tf 7.9048 0 0 7.4001 222.22 292.5099 Tm (au )Tj /T1_0 1 Tf 0.046 Tc 9 0 0 9 235.89 292.5099 Tm (are )Tj 0.05 Tc 9.2893 0 0 9 251.98 292.5099 Tm (the )Tj 0.0462 Tc 9 0 0 9 303.05 292.5099 Tm (isomorphisms )Tj -0.0209 Tc 6.558 0 Td (as )Tj 0.0458 Tc -37.191 -1.86 Td (noted )Tj 0.031 Tc 2.811 0 Td (above. )Tj 0.05 Tc 9.5493 0 0 9 83.08 275.77 Tm (Then )Tj 9.4259 0 0 9 107.8 275.77 Tm (the )Tj 9.2717 0 0 9 123.57 275.77 Tm (other )Tj 9.0048 0 0 9 148.13 275.77 Tm (half )Tj 0.0274 Tc 9 0 0 9 166.23 275.77 Tm (of )Tj 0.05 Tc 9.5625 0 0 9 176.74 275.77 Tm (the )Tj 0.0081 Tc 9 0 0 9 192.79 275.77 Tm (blocks )Tj -0.0029 Tc 3.018 0 Td (will )Tj 0.05 Tc 9.5181 0 0 9 237.07 275.77 Tm (be )Tj 9.1689 0 0 9 249.89 275.77 Tm (simply )Tj 9.5625 0 0 9 280.24 275.77 Tm (the )Tj 0.0274 Tc 9 0 0 9 323.37 275.59 Tm (of )Tj /T1_2 1 Tf 0.0263 Tc 9.7 0 0 9.7 334.35 275.59 Tm (D' )Tj /T1_0 1 Tf 0.05 Tc 9.0168 0 0 9 347.22 275.59 Tm (under )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 27.67 258.85 Tm (a)Tj 0.624 -0.275 Td (')Tj 0.368 0.275 Td (. )Tj /T1_0 1 Tf 0.05 Tc 9.9723 0 0 9 75.76 258.85 Tm (the )Tj 0.0417 Tc 9 0 0 9 92.68 258.85 Tm (two )Tj 0.0384 Tc 2.021 0 Td (halves )Tj 0.046 Tc 3.171 0 Td (are )Tj 0.033 Tc 1.762 0 Td (isomorphic. )Tj /T1_3 1 Tf 0.05 Tc 11.1445 0 0 8.7 206.15 258.85 Tm (It )Tj /T1_0 1 Tf -0.0299 Tc 9 0 0 9 216.65 258.85 Tm (is )Tj 0 Tc 1.058 0 Td (a )Tj 0.0427 Tc 0.868 0 Td (tedious )Tj 0.05 Tc 10.2677 0 0 9 266.23 258.85 Tm (but )Tj 0.0483 Tc 9 0 0 9 284.66 258.85 Tm (easy )Tj 0.05 Tc 9.787 0 0 9 305.98 258.85 Tm (matter )Tj 9.3858 0 0 9 336.94 258.85 Tm (to )Tj 0.0128 Tc 9 0 0 9 348.75 258.85 Tm (check )Tj 0.05 Tc 9.4124 0 0 9 27.52 241.75 Tm (that )Tj 0.0452 Tc 9 0 0 9 47.06 241.75 Tm (every )Tj 0.05 Tc 9.5632 0 0 9 71.83 241.75 Tm (pair )Tj -0.0299 Tc 9 0 0 9 91.73 241.75 Tm (is )Tj 0.0397 Tc 1.058 0 Td (covered )Tj 0.0161 Tc 7.28 0 Td (once. )Tj 0.05 Tc 9.239 0 0 9 41.14 224.83 Tm (The )Tj 0.0489 Tc 9 0 0 9 60.46 224.83 Tm (key )Tj 0.05 Tc 9.068 0 0 9 78.05 224.83 Tm (ingredients )Tj 9.1016 0 0 9 126.83 224.83 Tm (in )Tj 9.4259 0 0 9 138.22 224.83 Tm (the )Tj 0.0363 Tc 9 0 0 9 154.71 224.83 Tm (above )Tj 0.0437 Tc 2.98 0 Td (construction )Tj 0.0407 Tc 5.84 0 Td (are, )Tj 0.0204 Tc 2.019 0 Td (first, )Tj 0.0451 Tc 6.293 0 Td (S\(2,4,m\) )Tj 0.0256 Tc 4.257 0 Td (which )Tj 0.04 Tc -35.489 -1.88 Td (contain )Tj 0.0274 Tc 8.74 0 Td (of )Tj 0.05 Tc 9.1235 0 0 9 116.91 207.91 Tm (order )Tj /T1_2 1 Tf 8.933 0 0 8.9 140.87 207.91 Tm (u. )Tj /T1_0 1 Tf 0.0385 Tc 9 0 0 9 151.94 207.91 Tm (Such )Tj 0.0334 Tc 5.907 0 Td (exist )Tj -0.0026 Tc 2.34 0 Td (for )Tj 0.044 Tc 1.581 0 Td (any )Tj 0.05 Tc 9.0174 0 0 9 257.49 207.91 Tm (admissible )Tj /T1_2 1 Tf 9.3911 0 0 8.9 322.12 207.91 Tm (u, )Tj /T1_0 1 Tf 0 Tc 9 0 0 9 331.72 207.91 Tm (m )Tj -0.0209 Tc 1.232 0 Td (as )Tj 0.0127 Tc 1.181 0 Td (long )Tj -0.0209 Tc -36.201 -1.9 Td (as )Tj 0 Tc 1.188 0 Td (m )Tj -0.035 Tc 5.9785 0 0 9 49.38 190.81 Tm (;::: )Tj /T1_2 1 Tf 0.0411 Tc 9.2 0 0 9.2 58.95 190.81 Tm (3u )Tj /T1_3 1 Tf 0 Tc 13.6 0 0 13.6 70.7 190.81 Tm (+ )Tj /T1_0 1 Tf 9 0 0 9 79.79 190.81 Tm (1 )Tj -0.035 Tc 8.4666 0 0 9 88.18 190.81 Tm ([6]. )Tj 0.05 Tc 9.459 0 0 9 104.14 190.81 Tm (The )Tj 0.0381 Tc 9 0 0 9 123.17 190.81 Tm (second )Tj 0.0189 Tc 3.332 0 Td (key )Tj 0.0377 Tc 1.834 0 Td (ingredients )Tj 0.026 Tc 5.178 0 Td (are )Tj 0.05 Tc 9.066 0 0 9 231.1 190.81 Tm (transversal )Tj /T1_2 1 Tf 0.0297 Tc 9.7 0 0 9.7 311.02 190.81 Tm (TD\(k,4\) )Tj /T1_0 1 Tf 0.0206 Tc 9 0 0 9 347.21 190.81 Tm (which )Tj 0.036 Tc -35.509 -1.86 Td (are )Tj 0.0489 Tc 1.699 0 Td (equivalent )Tj 0.05 Tc 9.3858 0 0 9 88.54 174.0699 Tm (to )Tj 9.1816 0 0 9 123.57 174.0699 Tm (of )Tj 0.0456 Tc 9 0 0 9 134.91 174.0699 Tm (orthogonal )Tj 0.05 Tc 9.0977 0 0 9 182.08 174.0699 Tm (latin )Tj 0.0314 Tc 9 0 0 9 203.81 174.0699 Tm (squares )Tj 0.0474 Tc 3.624 0 Td (of )Tj 0.0428 Tc 1.24 0 Td (order )Tj /T1_1 1 Tf 0.0443 Tc 8.7 0 0 8.7 272.62 174.0699 Tm (k. )Tj /T1_0 1 Tf 0.05 Tc 9.2504 0 0 9 284.5 174.0699 Tm (These )Tj 0.0434 Tc 9 0 0 9 312.2 174.0699 Tm (exist )Tj 0.0074 Tc 2.5 0 Td (for )Tj 0.017 Tc 1.641 0 Td (all )Tj /T1_1 1 Tf -0.035 Tc 8.6597 0 0 8.7 362.98 174.0699 Tm (k, )Tj 0 Tc 9 0 0 9 27.99 157.1499 Tm (k )Tj /T1_2 1 Tf -0.035 Tc 6.1951 0 0 9 35.64 157.1499 Tm (=f )Tj /T1_0 1 Tf 0 Tc 9 0 0 9 44.77 157.1499 Tm (2 )Tj 0.0474 Tc 0.856 0 Td (or )Tj -0.035 Tc 8.8645 0 0 9 64.15 157.1499 Tm (6. )Tj 0.05 Tc 9.679 0 0 9 75.88 157.1499 Tm (The )Tj 9.114 0 0 9 95.32 157.1499 Tm (last )Tj 0.0496 Tc 9 0 0 9 112.97 157.1499 Tm (ingredient )Tj -0.035 Tc 8.7827 0 0 9 157.25 157.1499 Tm (is )Tj 0 Tc 9 0 0 9 166.77 157.1499 Tm (a )Tj 0.0354 Tc 0.821 0 Td (group )Tj 0.0211 Tc 2.92 0 Td (divisible )Tj 0.05 Tc 9.5548 0 0 9 264.41 157.1499 Tm (with )Tj 9.6991 0 0 9 286.36 157.1499 Tm (the )Tj 0.0478 Tc 9 0 0 9 302.75 157.1499 Tm (halving )Tj 0.05 Tc 9.128 0 0 9 335.71 157.1499 Tm (property )Tj 0.044 Tc 9 0 0 9 27.81 140.05 Tm (and )Tj 0.05 Tc 9.1746 0 0 9 45.09 140.05 Tm (our )Tj 9.4499 0 0 9 61.55 140.05 Tm (next )Tj 9.4909 0 0 9 83.08 140.05 Tm (lemma )Tj 0.0453 Tc 9 0 0 9 113.3 140.05 Tm (establishes )Tj 0.05 Tc 9.5625 0 0 9 159.82 140.05 Tm (the )Tj 0.0356 Tc 9 0 0 9 175.76 140.05 Tm (existence )Tj 0.0074 Tc 4.341 0 Td (of )Tj 0.0217 Tc 1.148 0 Td (two )Tj 0.0311 Tc 1.948 0 Td (such )Tj 0.0344 Tc 2.326 0 Td (designs. )Tj 0.05 Tc 10.285 0 0 8.8 28.02 115.39 Tm (Lemma )Tj 0 Tc 8.8 0 0 8.8 65.22 115.39 Tm (1 )Tj /T1_2 1 Tf 0.0356 Tc 9 0 0 9 76.68 115.39 Tm (There )Tj 0.0271 Tc 2.891 0 Td (exists )Tj 0 Tc 2.742 0 Td (a )Tj 0.0091 Tc 0.796 0 Td (group )Tj 0.0051 Tc 2.806 0 Td (divisible )Tj 0.0029 Tc 3.82 0 Td (design )Tj 0.0222 Tc 3.001 0 Td (with )Tj 0.0131 Tc 2.132 0 Td (the )Tj 0.0366 Tc 1.607 0 Td (halving )Tj 0.0448 Tc 3.539 0 Td (property )Tj 0.05 Tc 9.0883 0 0 9 323.03 115.39 Tm (on )Tj /T1_0 1 Tf -0.0286 Tc 9 0 0 9 335.21 115.39 Tm (16 )Tj /T1_2 1 Tf 0.0304 Tc 1.308 0 Td (points )Tj 0.0194 Tc -35.439 -1.9 Td (having )Tj 0.0191 Tc 3.134 0 Td (group )Tj 0.029 Tc 2.894 0 Td (size )Tj /T1_3 1 Tf 0 Tc 8.6 0 0 8.6 99.87 98.2899 Tm (4 )Tj /T1_2 1 Tf 0.0444 Tc 9 0 0 9 108.3 98.2899 Tm (and )Tj -0.0155 Tc 1.979 0 Td (block )Tj 0.0223 Tc 2.471 0 Td (size )Tj /T1_3 1 Tf -0.035 Tc 7.5363 0 0 8.6 165.76 98.2899 Tm (4\) )Tj /T1_2 1 Tf 0.0444 Tc 9 0 0 9 176.7 98.2899 Tm (and )Tj -0.0014 Tc 1.959 0 Td (one )Tj 0.0401 Tc 1.86 0 Td (on )Tj /T1_0 1 Tf -0.035 Tc 8.942 0 0 9 223.15 98.2899 Tm (24 )Tj /T1_2 1 Tf 0.0344 Tc 9 0 0 9 235.38 98.2899 Tm (points )Tj 0.05 Tc 9.1768 0 0 9 262.4 98.2899 Tm (with )Tj 0.0141 Tc 9 0 0 9 282.86 98.2899 Tm (group )Tj 0.0223 Tc 2.874 0 Td (size )Tj /T1_0 1 Tf 0 Tc 1.906 0 Td (3 )Tj /T1_2 1 Tf 0.0344 Tc 0.924 0 Td (and )Tj -0.0305 Tc 1.959 0 Td (block )Tj 0.0023 Tc -35.949 -1.901 Td (size )Tj -0.035 Tc 8.7232 0 0 9 45.28 81.1799 Tm (4. )Tj /T1_0 1 Tf 8.8017 0 0 8.9 190.75 48.97 Tm (232 )Tj ET endstream endobj 60 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 71685/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream 2*Dr;/b9r:#:9̐G3Gg2>Gș2:8D3#aȐdt|:#q:$菑'CCd|3Hb>\D{1A!!CI:I$ 9X` B !aܘ.XԱBOQe]Uf#<2ǰ&A 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