Strongly regular graphs on 400 - 499 vertices

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Parameters for strongly regular graphs on 400-499 vertices

The fields in the following table are all straightforward. The parameters are given in the standard (n,k,a,c) fashion. The eigenvalues of the adjacency matrix are called theta and tau with respective multiplicities m_theta and m_tau .

The Number field (will eventually) give some indication of the number of graphs known, the Type field indicates if the graph is a conference graph or a Smith graph (one of the Krein conditions is tight). Any further comments will be linked into the final column.

Parameters theta m_theta tau m_tau Number Type Comments
(400, 21, 2, 1) 5 175 -4 224 ?   none yet
(400, 38, 18, 2) 18 38 -2 361 ?   none yet
(400, 56, 6, 8) 6 224 -8 175 ?   none yet
(400, 57, 20, 6) 17 57 -3 342 ?   none yet
(400, 76, 24, 12) 16 76 -4 323 ?   none yet
(400, 84, 8, 20) 4 315 -16 84 ?   none yet
(400, 95, 30, 20) 15 95 -5 304 ?   none yet
(400, 105, 20, 30) 5 294 -15 105 ?   none yet
(400, 114, 38, 30) 14 114 -6 285 ?   none yet
(400, 126, 34, 42) 6 273 -14 126 ?   none yet
(400, 133, 42, 45) 8 224 -11 175 ?   none yet
(400, 133, 48, 42) 13 133 -7 266 ?   none yet
(400, 147, 50, 56) 7 252 -13 147 ?   none yet
(400, 152, 60, 56) 12 152 -8 247 ?   none yet
(400, 156, 74, 52) 26 48 -4 351 ?   none yet
(400, 168, 68, 72) 8 231 -12 168 ?   none yet
(400, 171, 74, 72) 11 171 -9 228 ?   none yet
(400, 189, 88, 90) 9 210 -11 189 ?   none yet
(400, 190, 90, 90) 10 190 -10 209 ?   none yet
(401, 200, 99, 100) 9.512 200 -10.512 200 ? Conf. none yet
(405, 96, 18, 24) 6 264 -12 140 ?   none yet
(405, 132, 63, 33) 33 30 -3 374 ?   none yet
(405, 196, 91, 98) 7 260 -14 144 ?   none yet
(405, 202, 100, 101) 9.562 202 -10.562 202 ? Conf. none yet
(406, 54, 27, 4) 25 28 -2 377 ?   none yet
(406, 108, 30, 28) 10 174 -8 231 ?   none yet
(406, 165, 68, 66) 11 174 -9 231 ?   none yet
(406, 189, 84, 91) 7 261 -14 144 ?   none yet
(406, 195, 96, 91) 13 145 -8 260 ?   none yet
(407, 126, 45, 36) 15 110 -6 296 ?   none yet
(408, 110, 28, 30) 8 220 -10 187 ?   none yet
(408, 176, 70, 80) 6 288 -16 119 ?   none yet
(409, 204, 101, 102) 9.612 204 -10.612 204 ? Conf. none yet
(411, 130, 45, 39) 13 137 -7 273 ?   none yet
(413, 112, 36, 28) 14 118 -6 294 ?   none yet
(414, 63, 12, 9) 9 161 -6 252 ?   none yet
(416, 100, 36, 20) 20 65 -4 350 ?   none yet
(416, 165, 64, 66) 9 220 -11 195 ?   none yet
(418, 147, 56, 49) 14 132 -7 285 ?   none yet
(421, 210, 104, 105) 9.759 210 -10.759 210 ? Conf. none yet
(424, 99, 26, 22) 11 159 -7 264 ?   none yet
(425, 72, 27, 9) 21 50 -3 374 ?   none yet
(425, 160, 60, 60) 10 204 -10 220 ?   none yet
(425, 212, 105, 106) 9.808 212 -10.808 212 ? Conf. none yet
(428, 112, 21, 32) 5 320 -16 107 ?   none yet
(429, 108, 27, 27) 9 208 -9 220 ?   none yet
(430, 39, 8, 3) 9 129 -4 300 ?   none yet
(430, 135, 36, 45) 6 300 -15 129 ?   none yet
(430, 165, 68, 60) 15 129 -7 300 ?   none yet
(433, 216, 107, 108) 9.904 216 -10.904 216 ? Conf. none yet
(435, 56, 28, 4) 26 29 -2 405 ?   none yet
(435, 154, 53, 55) 9 231 -11 203 ?   none yet
(435, 182, 73, 78) 8 260 -13 174 ?   none yet
(437, 100, 15, 25) 5 322 -15 114 ?   none yet
(438, 92, 31, 16) 19 72 -4 365 ?   none yet
(441, 40, 19, 2) 19 40 -2 400 ?   none yet
(441, 56, 7, 7) 7 216 -7 224 ?   none yet
(441, 60, 21, 6) 18 60 -3 380 ?   none yet
(441, 80, 25, 12) 17 80 -4 360 ?   none yet
(441, 88, 7, 20) 4 352 -17 88 ?   none yet
(441, 88, 35, 13) 25 44 -3 396 ?   none yet
(441, 100, 31, 20) 16 100 -5 340 ?   none yet
(441, 110, 19, 30) 5 330 -16 110 ?   none yet
(441, 120, 39, 30) 15 120 -6 320 ?   none yet
(441, 132, 33, 42) 6 308 -15 132 ?   none yet
(441, 140, 49, 42) 14 140 -7 300 ?   none yet
(441, 152, 43, 57) 5 342 -19 98 ?   none yet
(441, 154, 49, 56) 7 286 -14 154 ?   none yet
(441, 160, 61, 56) 13 160 -8 280 ?   none yet
(441, 176, 67, 72) 8 264 -13 176 ?   none yet
(441, 176, 85, 60) 29 48 -4 392 ?   none yet
(441, 180, 75, 72) 12 180 -9 260 ?   none yet
(441, 184, 87, 69) 23 72 -5 368 ?   none yet
(441, 190, 89, 76) 19 98 -6 342 ?   none yet
(441, 198, 87, 90) 9 242 -12 198 ?   none yet
(441, 200, 91, 90) 11 200 -10 240 ?   none yet
(441, 220, 95, 124) 3 396 -32 44 ?   none yet
(441, 220, 109, 110) 10.000 220 -11.000 220 ? Conf. none yet
(441, 220, 123, 96) 31 44 -4 396 ?   none yet
(442, 210, 99, 100) 10 221 -11 220 ?   none yet
(445, 222, 110, 111) 10.048 222 -11.048 222 ? Conf. none yet
(448, 150, 50, 50) 10 216 -10 231 ?   none yet
(448, 162, 66, 54) 18 105 -6 342 ?   none yet
(449, 224, 111, 112) 10.095 224 -11.095 224 ? Conf. none yet
(451, 130, 33, 39) 7 286 -13 164 ?   none yet
(451, 156, 57, 52) 13 164 -8 286 ?   none yet
(456, 65, 10, 9) 8 208 -7 247 ?   none yet
(456, 80, 4, 16) 4 360 -16 95 ?   none yet
(456, 104, 22, 24) 8 247 -10 208 ?   none yet
(456, 130, 24, 42) 4 380 -22 75 ?   none yet
(456, 140, 40, 44) 8 266 -12 189 ?   none yet
(456, 140, 58, 36) 26 56 -4 399 ?   none yet
(456, 175, 78, 60) 23 75 -5 380 ?   none yet
(456, 182, 73, 72) 11 208 -10 247 ?   none yet
(456, 195, 74, 90) 5 360 -21 95 ?   none yet
(457, 228, 113, 114) 10.189 228 -11.189 228 ? Conf. none yet
(459, 208, 82, 104) 4 390 -26 68 ?   none yet
(460, 85, 18, 15) 10 184 -7 275 ?   none yet
(460, 99, 18, 22) 7 275 -11 184 ?   none yet
(460, 147, 42, 49) 7 299 -14 160 ?   none yet
(460, 153, 32, 60) 3 414 -31 45 ?   none yet
(460, 204, 78, 100) 4 391 -26 68 ?   none yet
(460, 216, 116, 88) 32 45 -4 414 ?   none yet
(460, 225, 120, 100) 25 69 -5 390 ?   none yet
(461, 230, 114, 115) 10.235 230 -11.235 230 ? Conf. none yet
(465, 58, 29, 4) 27 30 -2 434 ?   none yet
(465, 144, 43, 45) 9 248 -11 216 ?   none yet
(465, 192, 72, 84) 6 340 -18 124 ?   none yet
(470, 126, 27, 36) 6 329 -15 140 ?   none yet
(474, 165, 52, 60) 7 315 -15 158 ?   none yet
(475, 90, 25, 15) 15 114 -5 360 ?   none yet
(475, 96, 32, 16) 20 75 -4 399 ?   none yet
(476, 133, 42, 35) 14 152 -7 323 ?   none yet
(476, 133, 60, 28) 35 34 -3 441 ?   none yet
(477, 140, 31, 45) 5 371 -19 105 ?   none yet
(477, 168, 57, 60) 9 264 -12 212 ?   none yet
(477, 238, 118, 119) 10.420 238 -11.420 238 ? Conf. none yet
(481, 240, 119, 120) 10.466 240 -11.466 240 ? Conf. none yet
(483, 240, 118, 120) 10 252 -12 230 ?   none yet
(484, 42, 20, 2) 20 42 -2 441 ?   none yet
(484, 63, 22, 6) 19 63 -3 420 ?   none yet
(484, 84, 26, 12) 18 84 -4 399 ?   none yet
(484, 92, 6, 20) 4 391 -18 92 ?   none yet
(484, 105, 14, 25) 5 363 -16 120 ?   none yet
(484, 105, 32, 20) 17 105 -5 378 ?   none yet
(484, 115, 18, 30) 5 368 -17 115 ?   none yet
(484, 126, 40, 30) 16 126 -6 357 ?   none yet
(484, 138, 32, 42) 6 345 -16 138 ?   none yet
(484, 138, 47, 36) 17 120 -6 363 ?   none yet
(484, 147, 50, 42) 15 147 -7 336 ?   none yet
(484, 161, 48, 56) 7 322 -15 161 ?   none yet
(484, 168, 62, 56) 14 168 -8 315 ?   none yet
(484, 184, 66, 72) 8 299 -14 184 ?   none yet
(484, 189, 76, 72) 13 189 -9 294 ?   none yet
(484, 207, 86, 90) 9 276 -13 207 ?   none yet
(484, 210, 92, 90) 12 210 -10 273 ?   none yet
(484, 230, 108, 110) 10 253 -12 230 ?   none yet
(484, 231, 110, 110) 11 231 -11 252 ?   none yet
(485, 242, 120, 121) 10.511 242 -11.511 242 ? Conf. none yet
(486, 97, 16, 20) 7 291 -11 194 ?   none yet
(486, 100, 22, 20) 10 210 -8 275 ?   none yet
(486, 165, 36, 66) 3 440 -33 45 ? Smith none yet
(486, 194, 67, 84) 5 388 -22 97 ?   none yet
(486, 210, 99, 84) 21 100 -6 385 ?   none yet
(490, 144, 28, 48) 4 414 -24 75 ?   none yet
(490, 165, 56, 55) 11 225 -10 264 ?   none yet
(490, 192, 92, 64) 32 49 -4 440 ?   none yet
(493, 246, 122, 123) 10.602 246 -11.602 246 ? Conf. none yet
(494, 85, 12, 15) 7 285 -10 208 ?   none yet
(495, 38, 1, 3) 5 285 -7 209 ?   none yet
(495, 78, 29, 9) 23 54 -3 440 ?   none yet
(495, 104, 28, 20) 14 143 -6 351 ?   none yet
(495, 190, 53, 85) 3 450 -35 44 ?   none yet
(495, 190, 85, 65) 25 76 -5 418 ?   none yet
(495, 208, 86, 88) 10 260 -12 234 ?   none yet
(495, 234, 93, 126) 3 450 -36 44 ?   none yet
(495, 238, 109, 119) 7 340 -17 154 ?   none yet
(496, 54, 4, 6) 6 279 -8 216 ?   none yet
(496, 60, 30, 4) 28 31 -2 464 ?   none yet
(496, 110, 18, 26) 6 341 -14 154 ?   none yet
(496, 135, 38, 36) 11 216 -9 279 ?   none yet
(496, 198, 80, 78) 12 216 -10 279 ?   none yet
(496, 231, 102, 112) 7 341 -17 154 ?   none yet
(496, 240, 120, 112) 16 155 -8 340 ?   none yet
(497, 186, 55, 78) 4 426 -27 70 ?   none yet
(497, 240, 127, 105) 27 70 -5 426 ?   none yet
(498, 161, 64, 46) 23 83 -5 414 ?   none yet