Please see the new website: http://pietereendebak.nl/oapackage.
On this page we present numbers of non-isomorphic orthogonal arrays for many series. Most of them are generated by our Orthogonal Arrays program, some series are generated by hand. The algorithm used is described in our paper Complete Enumeration of Pure-Level and Mixed-Level Orthogonal Arrays, Journal of Combinatorial Designs, Volume 18, Issue 2, pages 123-140, 2010.
Software for manipulating the arrays can be found here. To obtain the actual arrays (for the larger series several GB of data), please contact one of the authors above.
The research leading to these results was performed at the Computer Vision and Statistics group of TNO and the Department of Mathematics, Statistics, and Actuarial Sciences of University of Antwerp.
For an introduction to orthogonal arrays see the book Orthogonal Arrays: Theory and Applications by Hedayat, Sloane and Stufken.
OA(4; 2; 2a)
: 1, 0
OA(8; 2; 2a)
: 2, 2, 1, 1, 1, 0
OA(8; 2; 412a)
: 1, 1, 1, 0
OA(9; 2; 3a)
: 1, 1, 0
OA(12; 2; 2a)
: 2, 1, 2, 2, 1, 1, 1, 1, 1, 0
OA(12; 2; 312a)
: 2, 3, 1, 0
OA(12; 2; 612a)
: 1, 0
OA(16; 2; 2a)
: 3, 5, 11, 27, 55, 80, 87, 78, 58, 36, 18, 10, 5, 0
OA(16; 2; 412a)
: 3, 10, 28, 65, 110, 123, 110, 72, 38, 15, 8, 0
OA(16; 2; 4a)
: 2, 1, 1, 0
OA(16; 2; 442a)
: 2, 1, 1, 1, 1, 0
OA(16; 2; 432a)
: 2, 2, 4, 4, 4, 2, 2, 0
OA(16; 2; 422a)
: 2, 7, 17, 27, 30, 25, 14, 6, 3, 0
OA(16; 2; 812a)
: 1, 1, 2, 1, 1, 1, 1, 0
OA(18; 2; 213a)
: 3, 15, 48, 19, 12, 3, 0
OA(18; 2; 3a)
: 4, 12, 10, 8, 3, 0
OA(18; 2; 613a)
: 2, 3, 1, 1, 1
OA(20; 2; 2a)
: 3, 3, 11, 75, 474, 1603, 2477, 2389, 1914, 1300, 730, 328, 124, 40, 11, 6, 3, 0
OA(20; 2; 512a)
: 3, 10, 15, 38, 30, 4, 1, 0
OA(20; 2; 512a)
: 3, 10, 15, 38, 30, 4, 1, 0
OA(20; 2; 1012a)
: 1, 0
OA(24; 2; 2a)
: 4, 10, 63, 1350, 57389, 1470157, 12952435, 38592861, 52912678, 51154497, 43092737, 31833387, 19960039, 10351396, 4385567, 1502242, 409478, 86725, 13833, 1604, 130, 0
OA(24; 2; 312a)
: 4, 29, 573, 28745, 1089168, 14576216, 57436095, 71157023, 33893515, 10266252, 3305030, 981180, 220993, 32567, 2282, 0
OA(24; 2; 412a)
: 4, 25, 552, 21757, 457768, 3113669, 8168256, 12605571, 15119461, 14961206, 12096092, 7855020, 4066838, 1665918, 532484, 129122, 22880, 2758, 238, 0
OA(24; 2; 41312a)
: 5, 131, 6412, 226330, 2360583, 6467858, 5404183, 2341404, 963413, 350559, 94228, 16238, 1282, 0
OA(24; 2; 612a)
: 4, 25, 226, 2663, 19323, 58112, 65679, 26454, 12243, 4882, 1543, 277, 45, 0
OA(24; 2; 61412a)
: 3, 38, 400, 2060, 3911, 2200, 1357, 689, 283, 64, 14, 0
OA(24; 2; 1212a)
: 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0
OA(25; 2; 5a)
: 2, 1, 1, 1
OA(27; 2; 3a)
: 9, 711, 187188, 922548, 157829, 21688, 9793, 3766, 1252, 341, 68, 0
OA(27; 2; 913a)
: 2, 7, 10, 13, 12, 9, 5, 4, 0
OA(28; 2; 2a)
: 4, 7, 127, 17826, 5882186, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(28; 2; 712a)
: 4, 25, 371, 21502, 395598, 1422094, 1005490, 135569, 4296, 104, 21, 0
OA(30; 2; 513121)
: 6
OA(32; 2; 2a)
: 5, 19, 491, 266217, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(32; 2; 412a)
: 7, 158, 57857, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(32; 2; 4a)
: 44, 32983, 108339, 31779, 6564, 283, 20, 0
OA(32; 2; 462a)
: 44, 32983, 108339, 31779, 582942, 3880455, 17714295, 52127662, 105510372, 152752321, 162022665, 127424325, 74302445, 31659282, 9492964, 1841598, 183833, 0
OA(32; 2; 472a)
: 44, 32983, 108339, 31779, 6564, 70932, 342203, 969642, 1770830, 2208501, 1920008, 1172827, 491748, 132333, 19379, 0
OA(32; 2; 482a)
: 44, 32983, 108339, 31779, 6564, 283, 1549, 4098, 6522, 6607, 4282, 1727, 362, 0
OA(32; 2; 492a)
: 44, 32983, 108339, 31779, 6564, 283, 20, 86, 116, 86, 40, 0
OA(32; 2; 432a)
: 44, 32804, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(32; 2; 422a)
: 12, 2548, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(32; 2; 81462a)
: 10, 89, 200, 70, 22, 67, 137, 177, 137, 67, 22, 0
OA(32; 2; 81472a)
: 10, 89, 200, 70, 22, 1, 1, 1, 1, 0
OA(32; 2; 81452a)
: 10, 89, 200, 70, 489, 1848, 4226, 6331, 6515, 4667, 2274, 718, 130, 0
OA(32; 2; 81442a)
: 10, 89, 200, 1978, 12452, 47738, 123554, 220792, 281678, 259750, 176744, 87561, 31595, 7552, 1213, 0
OA(36; 2; 2a)
: 5, 15, 1242, 3352529, ?, ?, ?, ?
OA(36; 2; 312a)
: 6, 138, 130852, ?, ?, ?
OA(36; 2; 322a)
: 9, 1774, ?, ?, ?, ?
OA(36; 2; 3a)
: 24, 221510, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(36; 2; 6a)
: 12, 0
OA(36; 2; 633a)
: 12, 274, 579, 550, 288, 38, 23, 8, 0
OA(36; 2; 63312a)
: 12, 274, 2212, 5272, 1208, 147, 0
OA(36; 2; 632a)
: 12, 131, 3456, 13132, 11014, 3159, 761, 118, 8, 0
OA(42; 2; 713121)
: 12
OA(70; 2; 715121)
: 1897
OA(8; 3; 2a)
: 1, 0
OA(16; 3; 2a)
: 2, 2, 1, 1, 1, 0
OA(16; 3; 412a)
: 1, 0
OA(24; 3; 2a)
: 2, 1, 2, 1, 1, 1, 1, 1, 1, 0
OA(24; 3; 312a)
: 2, 3, 0
OA(24; 3; 612a)
: 1, 0
OA(27; 3; 3a)
: 1, 0
OA(32; 3; 2a)
: 3, 5, 10, 17, 33, 34, 32, 22, 23, 12, 10, 5, 5, 0
OA(32; 3; 412a)
: 3, 7, 7, 11, 8, 0
OA(32; 3; 422a)
: 2, 2, 2, 0
OA(32; 3; 812a)
: 1, 0
OA(36; 3; 322a)
: 3
OA(40; 3; 2a)
: 3, 3, 9, 25, 105, 213, 353, 260, 235, 132, 96, 36, 26, 7, 6, 3, 3, 0
OA(40; 3; 512a)
: 3, 7, 1, 1, 0
OA(40; 3; 1012a)
: 1, 0
OA(48; 3; 2a)
: 4, 10, 45, 397, 8383, 166081, 1310006, 3528089, 4460865, 3980095, 3139653, 2165144, 1288460, 629705, 259346, 84495, 24012, 4919, 1129, 130, 60, 0
OA(48; 3; 312a)
: 4, 21, 134, 938, 3056, 5018, 3, 0
OA(48; 3; 412a)
: 4, 4, 24, 98, 387, 1362, 2595, 2217, 560, 0
OA(48; 3; 41312a)
: 5, 35, 19, 0
OA(48; 3; 612a)
: 4, 14, 30, 74, 45, 0
OA(48; 3; 61412a)
: 3, 0
OA(48; 3; 1212a)
: 1, 0
OA(54; 3; 213a)
: 5, 33, 4, 0
OA(54; 3; 3a)
: 7, 4, 0
OA(54; 3; 613a)
: 2
OA(56; 3; 2a)
: 4, 7, 86, 4049, 757190, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(56; 3; 712a)
: 4, 14, 7, 10
OA(56; 3; 1412a)
: 1, 0
OA(60; 3; 51312a)
: 6
OA(64; 3; 2a)
: 5, 19, 358, 91789, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(64; 3; 412a)
: 7, 75, 4101, 251617, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(64; 3; 4a)
: 5, 1, 1, 0
OA(64; 3; 462a)
: 5, 1, 1, 0
OA(64; 3; 452a)
: 5, 1, 1, 1, 0
OA(64; 3; 442a)
: 5, 3, 5, 3, 3, 1, 1, 0
OA(64; 3; 432a)
: 10, 107, 237, 255, 126, 35, 12, 2, 0
OA(64; 3; 422a)
: 12, 267, 13903, 104949, 175297, 151708, 138825, 83409, 35807, 10030, 2159, 0
OA(64; 3; 812a)
: 5, 26, 192, 1146, 924, 0
OA(64; 3; 81412a)
: 4
OA(64; 3; 1612a)
: 1, 0
OA(72; 3; 322a)
: 9, 465, 380253, 32565625, 10620268, 953145, 653569, 207970, 22833, 69, 27, 0
OA(72; 3; 413221)
: 18
OA(72; 3; 61312a)
: 10, 265, 293, 0
OA(72; 3; 622a)
: 6, 0
OA(72; 3; 912a)
: 5, 26, 96, 498, 0
OA(80; 3; 2a)
: 6, 33, 3494, ?, ?, ?, ?
OA(80; 3; 51412a)
: 26, 3127, 409509, 217319, 4814, 0
OA(81; 3; 3a)
: 32, 17056, 1099, 486, 235, 1, 1, 0
OA(81; 3; 913a)
: 3, 2, 0
OA(84; 3; 71312a)
: 12
OA(88; 3; 2a)
: 6, 28, 11041, ?, ?, ?, ?, ?, ?, ?, ?
OA(90; 3; 513221)
: 39
OA(96; 3; 2a)
: 7, 56, 39739, ?, ?, ?, ?, ?, ?, ?, ?
OA(96; 3; 312a)
: 9, 487, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(100; 3; 522a)
: 61
OA(104; 3; 2a)
: 7, 49, 128458, ?, ?, ?, ?, ?, ?, ?, ?
OA(108; 3; 322a)
: 20
OA(108; 3; 332a)
: 39, 5384016
OA(108; 3; 613221)
: 122
OA(112; 3; 71412a)
: 129
OA(120; 3; 51413121)
: 2395
OA(120; 3; 61512a)
: 422
OA(150; 3; 523121)
: 84422
OA(176; 3; 2a)
: 12, 432, ?, ?, ?, ?, ?, ?, ?, ?, ?
OA(16; 4; 2a)
: 1, 0
OA(32; 4; 2a)
: 2, 2, 0
OA(32; 4; 412a)
: 1, 0
OA(48; 4; 2a)
: 2, 0
OA(48; 4; 312a)
: 2, 3, 0
OA(48; 4; 612a)
: 1
OA(64; 4; 2a)
: 3, 5, 7, 3, 0
OA(64; 4; 412a)
: 3, 7, 2, 0
OA(64; 4; 422a)
: 2
OA(64; 4; 812a)
: 1
OA(72; 4; 322a)
: 3
OA(80; 4; 2a)
: 3, 1
OA(80; 4; 512a)
: 3, 7
OA(81; 4; 3a)
: 1
OA(96; 4; 2a)
: 4, 9, 4, 0
OA(96; 4; 312a)
: 4, 21, 64, 5, 0
OA(96; 4; 412a)
: 4, 1, 0
OA(96; 4; 41312a)
: 5, 35
OA(96; 4; 612a)
: 4, 14, 0
OA(96; 4; 61412a)
: 3, 0
OA(108; 4; 332a)
: 5
OA(112; 4; 2a)
: 4, 3
OA(112; 4; 712a)
: 4, 14
OA(120; 4; 51312a)
: 6
OA(128; 4; 2a)
: 5, 17, 123, 1288, 4132, 1683, 477, 2, 1, 1, 1, 0
OA(128; 4; 412a)
: 7, 75, 870, 2649, 1014, 275, 0
OA(128; 4; 432a)
: 10, 6, 0
OA(128; 4; 422a)
: 12, 198, 202, 77, 0
OA(128; 4; 812a)
: 5, 26, 19, 11, 10, 0
OA(128; 4; 81412a)
: 4, 0
OA(128; 4; 1612a)
: 1, 0
OA(144; 4; 2a)
: 5, 7, 35, 20, 0
OA(144; 4; 312a)
: 6, 78, 130, 0
OA(144; 4; 322a)
: 9, 319, 11232, 0
OA(144; 4; 41322a)
: 18
OA(144; 4; 612a)
: 6, 0
OA(144; 4; 61312a)
: 10, 265
OA(144; 4; 622a)
: 6, 0
OA(144; 4; 912a)
: 5, 26, 0
OA(160; 4; 2a)
: 6, 29, 450, 99618, ?, ?, ?
OA(160; 4; 412a)
: 9, 43, 1965, 534, 0
OA(160; 4; 512a)
: 9, 230, 11016, 19153, 0
OA(160; 4; 51412a)
: 26, 2277, 28, 0
OA(160; 4; 1012a)
: 6, ?, ?
OA(162; 4; 3a)
: 14, 0
OA(162; 4; 3521)
: 14, 46
OA(162; 4; 3421)
: 13
OA(168; 4; 71312a)
: 12
OA(176; 4; 2a)
: 6, 14, 945, ?, ?, ?, ?, ?, ?, ?
OA(180; 4; 51322a)
: 39
OA(200; 4; 522a)
: 61
OA(216; 4; 332a)
: 39, 464307
OA(216; 4; 413321)
: 215
OA(216; 4; 61322a)
: 122
OA(252; 4; 71322a)
: 308
OA(256; 4; 4a)
: 26, 0
OA(256; 4; 452a)
: 26, 0
OA(32; 5; 2a)
: 1, 0
OA(64; 5; 2a)
: 2, 2, 0
OA(64; 5; 412a)
: 1, 0
OA(96; 5; 2a)
: 2, 0
OA(96; 5; 312a)
: 2, 3, 0
OA(128; 5; 2a)
: 3, 5, 7, 2, 0
OA(128; 5; 412a)
: 3, 7, 0
OA(128; 5; 422a)
: 2, 0
OA(128; 5; 812a)
: 1, 0
OA(144; 5; 322a)
: 3
OA(160; 5; 2a)
: 3, 1, 0
OA(160; 5; 512a)
: 3, 7, 0
OA(192; 5; 2a)
: 4, 9, 3, 0
OA(192; 5; 312a)
: 4, 21, 64, 0
OA(192; 5; 412a)
: 4, 0
OA(192; 5; 41312a)
: 5, 35, 0
OA(192; 5; 612a)
: 4, 14, 0
OA(192; 5; 61412a)
: 3, 0
OA(216; 5; 332a)
: 5
OA(224; 5; 2a)
: 4, 3, 0
OA(224; 5; 712a)
: 4, 14, 0
OA(240; 5; 51312a)
: 6
OA(256; 5; 422a)
: 12, 198, 10, 0
OA(256; 5; 432a)
: 10, 0
OA(288; 5; 41322a)
: 18
OA(360; 5; 51322a)
: 39
OA(384; 5; 412a)
: 14, 827, 2644, 0
OA(64; 6; 2a)
: 1, 0
OA(128; 6; 2a)
: 2, 2, 0
OA(128; 6; 412a)
: 1, 0
OA(192; 6; 2a)
: 2, 0
OA(192; 6; 312a)
: 2, 3, 0
OA(256; 6; 2a)
: 3, 5, 7, 0
OA(256; 6; 412a)
: 3, 7, 0
OA(256; 6; 422a)
: 2, 0
OA(288; 6; 322a)
: 3
OA(320; 6; 2a)
: 3, 0
OA(384; 6; 2a)
: 4, 9, 1, 0
OA(384; 6; 312a)
: 4, 21, 64, 0
OA(384; 6; 412a)
: 4, 0
OA(384; 6; 41312a)
: 5, 35, 0
OA(128; 7; 2a)
: 1, 0
OA(256; 7; 2a)
: 2, 2, 0
OA(256; 7; 412a)
: 1, 0
OA(384; 7; 2a)
: 2, 0
OA(384; 7; 312a)
: 2, 3, 0
OA(384; 7; 612a)
: 1, 0
OA(512; 7; 2a)
: 3, 5, 7, 0
OA(512; 7; 412a)
: 3, 7, 0
OA(512; 7; 422a)
: 2, 0
OA(256; 8; 2a)
: 1, 0
OA(512; 8; 2a)
: 2, 2, 0
OA(512; 8; 412a)
: 1, 0