Near optimal Golomb rulers with 16 marks

This list includes mirror rulers and is sorted by length and by the first differences.


{ /* OGR-16*/

{0,  1,  4, 11, 26, 32, 56, 68, 76,115,117,134,150,163,168,177},
{0,  9, 14, 27, 43, 60, 62,101,109,121,145,151,166,173,176,177},

{0,  2,  5, 15, 46, 70, 91,100,107,126,127,149,160,166,174,178},
{0,  4, 12, 18, 29, 51, 52, 71, 78, 87,108,132,163,173,176,178},

{0,  1,  4, 14, 33, 40, 55, 64, 85,101,112,154,159,171,177,179},
{0,  2,  8, 20, 25, 67, 78, 94,115,124,139,146,165,175,178,179},
{0,  2, 10, 14, 17, 46, 47, 70, 96,101,112,121,139,160,173,179},
{0,  3, 11, 13, 28, 44, 76, 83,112,113,118,132,136,158,170,179},
{0,  6, 19, 40, 58, 67, 78, 83,109,132,133,162,165,169,177,179},
{0,  9, 21, 43, 47, 61, 66, 67, 96,103,135,151,166,168,176,179},

{0,  1,  7, 23, 51, 60, 85,105,109,140,148,151,161,166,178,180},
{0,  1, 10, 12, 17, 53, 57, 77, 83,108,116,131,145,158,177,180},
{0,  2, 14, 19, 29, 32, 40, 71, 75, 95,120,129,157,173,179,180},
{0,  3, 22, 35, 49, 64, 72, 97,103,123,127,163,168,170,179,180},
{0,  4, 14, 16, 23, 59, 76, 96,111,124,142,150,153,174,175,180},
{0,  5,  6, 27, 30, 38, 56, 69, 84,104,121,157,164,166,176,180},

{0,  1, 19, 28, 35, 58, 61, 71, 82,130,135,150,167,175,179,181},
{0,  2,  5, 17, 23, 30, 49, 57, 71,107,108,117,146,150,170,181},
{0,  2,  6, 14, 31, 46, 51, 99,110,120,123,146,153,162,180,181},
{0,  2, 16, 22, 39, 43, 52, 71, 83,117,118,125,128,143,176,181},
{0,  3,  5, 23, 35, 36, 62, 87,103,109,143,153,157,164,172,181},
{0,  3, 10, 15, 26, 43, 72, 91,121,122,130,143,157,175,177,181},
{0,  4,  6, 24, 38, 51, 59, 60, 90,109,138,155,166,171,178,181},
{0,  4, 14, 15, 17, 37, 46, 76, 82,100,126,134,153,169,174,181},
{0,  5, 38, 53, 56, 63, 64, 98,110,129,138,142,159,165,179,181},
{0,  7, 12, 28, 47, 55, 81, 99,105,135,144,164,166,167,177,181},
{0,  9, 17, 24, 28, 38, 72, 78, 94,119,145,146,158,176,178,181},
{0, 11, 31, 35, 64, 73, 74,110,124,132,151,158,164,176,179,181},

{0,  1,  7, 17, 19, 51, 73, 94,103,114,118,143,151,156,179,182},
{0,  1,  9, 19, 50, 56, 67, 80,101,113,139,153,155,175,178,182},
{0,  1, 13, 17, 28, 63, 84,103,121,127,141,150,172,175,180,182},
{0,  1, 15, 28, 36, 54, 59, 84,101,130,141,163,173,175,179,182},
{0,  2,  7, 10, 32, 41, 55, 61, 79, 98,119,154,165,169,181,182},
{0,  2, 12, 19, 43, 61, 64, 77, 99,100,127,153,167,173,178,182},
{0,  3,  4, 12, 23, 44, 69, 74, 87,121,123,137,147,154,176,182},
{0,  3,  4, 20, 28, 43, 49, 76, 85,111,123,145,164,175,177,182},
{0,  3,  7,  9, 19, 41, 52, 81, 98,123,128,146,154,167,181,182},
{0,  3, 26, 31, 39, 64, 68, 79, 88,109,131,163,165,175,181,182},
{0,  4,  7, 27, 29, 43, 69, 81,102,115,126,132,163,173,181,182},
{0,  4,  9, 15, 29, 55, 82, 83,105,118,121,139,163,170,180,182},
{0,  5,  7, 18, 37, 59, 71, 97,106,133,139,154,162,178,179,182},
{0,  6, 28, 35, 45, 59, 61, 95,108,113,138,159,170,178,179,182},

{0,  1,  3, 15, 57, 64, 80,102,112,131,139,148,152,172,178,183},
{0,  1,  3, 20, 25, 35, 61, 72,103,110,126,156,165,169,177,183},
{0,  1,  5, 17, 19, 28, 43, 64, 77,112,118,143,151,173,180,183},
{0,  1,  5, 27, 34, 45, 58, 77, 93,113,123,160,162,174,177,183},
{0,  1,  8, 13, 23, 43, 64, 82, 88,122,126,155,158,172,174,183},
{0,  1,  9, 13, 42, 57, 67, 87,118,140,146,157,164,178,180,183},
{0,  1,  9, 22, 29, 48, 80, 85, 91,116,126,150,166,168,180,183},
{0,  1, 16, 27, 30, 61, 66, 83,107,115,135,158,170,177,179,183},
{0,  1, 17, 19, 30, 40, 64, 89, 97,125,139,145,171,176,180,183},
{0,  2,  3,  9, 27, 41, 56, 69, 89, 99,115,120,160,164,172,183},
{0,  2,  3, 21, 33, 73, 79, 87,115,122,132,154,159,170,179,183},
{0,  2,  3, 27, 34, 49, 63, 69, 82, 86,127,139,157,167,178,183},
{0,  2,  6, 21, 37, 61, 84,112,113,125,151,158,161,169,178,183},
{0,  2,  7, 33, 42, 55, 56, 85,101,126,145,162,165,173,177,183},
{0,  3,  5, 19, 26, 37, 43, 65, 96,116,126,141,170,174,182,183},
{0,  3,  5, 20, 43, 50, 74, 85,106,122,147,155,161,173,174,183},
{0,  3,  7, 12, 38, 44, 58, 86, 94,119,143,153,164,166,182,183},
{0,  3, 10, 32, 40, 65, 71,106,119,140,155,164,166,178,182,183},
{0,  3, 15, 17, 33, 57, 67, 92, 98,103,135,154,161,174,182,183},
{0,  4,  6, 13, 25, 48, 68, 76,100,117,122,153,156,167,182,183},
{0,  4,  7, 13, 34, 39, 54, 85, 96,110,118,154,155,171,173,183},
{0,  4, 13, 24, 29, 51, 61, 68, 96,104,110,150,162,180,181,183},
{0,  5, 11, 31, 35, 44, 52, 71, 81,103,119,126,168,180,182,183},
{0,  5, 14, 22, 25, 32, 58, 70, 71, 99,122,146,162,177,181,183},
{0,  5, 15, 34, 35, 42, 73, 75, 86, 89, 98,134,151,155,177,183},
{0,  5, 16, 26, 44, 56, 97,101,114,120,134,149,156,180,181,183},
{0,  6,  9, 21, 23, 60, 70, 90,106,125,138,149,156,178,182,183},
{0,  6, 10, 18, 21, 38, 57, 82, 98,127,128,141,150,176,181,183},
{0,  6, 14, 18, 27, 57, 73, 80,111,122,148,158,163,180,182,183},
{0,  6, 28, 32, 49, 85, 94, 97,108,110,141,148,149,168,178,183},
{0,  9, 10, 22, 28, 36, 61, 77, 98,109,133,140,163,178,180,183},
{0,  9, 11, 25, 28, 57, 61, 95,101,119,140,160,170,175,182,183},
{0, 10, 11, 31, 33, 58, 70, 73, 77, 86,122,127,151,157,165,183},
{0, 10, 12, 28, 29, 65, 73, 87, 98,129,144,149,170,176,179,183},
{0, 11, 19, 23, 63, 68, 84, 94,114,127,142,156,174,180,181,183},
{0, 18, 26, 32, 56, 61, 97,106,110,113,125,150,152,172,173,183},

{0,  1,  3, 14, 30, 39, 62, 96,104,111,116,137,156,174,180,184},
{0,  1,  3, 18, 50, 55, 64, 74, 85,112,143,151,155,171,177,184},
{0,  1,  4, 15, 21, 46, 59, 69, 81, 99,132,148,156,175,182,184},
{0,  1,  4, 29, 39, 47, 70, 87,106,120,150,162,171,177,182,184},
{0,  1,  7, 10, 28, 45, 75, 88,107,121,129,144,155,160,180,184},
{0,  1,  7, 22, 26, 31, 54, 66, 83, 93,126,134,168,171,182,184},
{0,  1,  9, 28, 53, 57, 59, 73, 91,108,138,151,162,174,177,184},
{0,  1, 10, 18, 31, 33, 68, 84, 96,132,138,143,157,177,181,184},
{0,  1, 12, 14, 20, 49, 65, 82, 91,123,141,145,148,169,179,184},
{0,  2,  6, 13, 27, 43, 55, 81,100,115,120,144,166,167,176,184},
{0,  2,  7, 13, 22, 34, 64, 78, 97,114,137,145,155,180,183,184},
{0,  2,  8, 13, 27, 36, 56, 82,106,121,122,139,143,174,181,184},
{0,  2,  9, 10, 33, 47, 50, 69, 96,111,122,150,154,166,179,184},
{0,  2,  9, 26, 34, 38, 61, 82,100,115,137,165,168,178,179,184},
{0,  2,  9, 28, 36, 52, 85,103,115,125,138,163,169,180,183,184},
{0,  2, 11, 24, 25, 55, 76, 95,105,111,123,138,143,177,180,184},
{0,  2, 13, 16, 50, 58, 91,101,118,130,153,158,162,177,183,184},
{0,  3,  7, 27, 41, 46, 52, 88,100,116,151,153,166,174,183,184},
{0,  3, 10, 41, 45, 62, 63, 78,102,128,148,157,171,176,182,184},
{0,  4,  7,  9, 27, 41, 51, 84, 96,113,124,132,162,163,178,184},
{0,  4,  7, 41, 46, 61, 73, 79, 89,108,129,159,160,173,182,184},
{0,  4, 10, 28, 47, 68, 73, 80, 88,122,145,154,170,181,183,184},
{0,  4, 17, 19, 39, 40, 69, 93,100,111,127,137,170,175,178,184},
{0,  4, 23, 28, 35, 67, 69, 80,120,128,142,157,158,175,178,184},
{0,  4, 24, 29, 40, 55, 63, 77, 96,109,139,156,174,177,183,184},
{0,  5,  6, 16, 19, 47, 69, 84,102,123,146,150,158,175,182,184},
{0,  5,  8, 14, 41, 56, 63, 67, 95,124,140,141,159,161,171,184},
{0,  5,  9, 17, 20, 46, 56, 77, 79,101,117,131,159,165,166,184},
{0,  5, 15, 36, 39, 43, 61, 93,102,119,135,164,170,172,183,184},
{0,  5, 18, 30, 34, 62, 73, 88,115,134,137,151,174,175,182,184},
{0,  6,  9, 14, 47, 57, 73, 84, 91,115,144,145,165,167,180,184},
{0,  6,  9, 26, 27, 42, 56, 64,104,115,117,149,156,161,180,184},
{0,  6, 13, 15, 42, 45, 56, 79, 89,107,138,159,160,164,176,184},
{0,  6, 21, 22, 52, 60, 71, 88,100,133,143,157,175,177,180,184},
{0,  7, 10, 22, 33, 46, 76, 93,111,125,127,131,156,175,183,184},
{0,  7, 13, 29, 33, 41, 72, 99,110,120,129,134,166,181,183,184},
{0,  8, 17, 18, 40, 64, 69, 84,103,129,141,157,171,178,182,184},
{0,  8, 20, 24, 25, 46, 77, 95,105,128,139,142,169,171,178,184},
{0, 11, 32, 33, 60, 68, 75, 77, 80,106,131,147,161,165,171,184},
{0, 13, 19, 23, 37, 53, 78,104,107,109,116,124,151,152,173,184},
{0, 13, 23, 25, 43, 44, 60, 89,117,121,128,143,170,176,179,184},
{0, 18, 19, 25, 53, 67, 83,105,107,128,138,164,167,175,179,184},

{0,  1,  3, 20, 27, 35, 77, 83,113,123,144,156,167,172,181,185},
{0,  1,  3, 22, 46, 53, 61, 88,108,118,144,156,167,172,181,185},
{0,  1,  5, 17, 24, 27, 64, 75, 89,107,135,141,143,156,176,185},
{0,  1,  5, 18, 24, 34, 60, 81,101,131,139,146,171,174,183,185},
{0,  1,  6,  8, 40, 52, 62, 77,100,119,135,155,164,168,182,185},
{0,  1,  6, 13, 34, 36, 45, 61, 76,114,117,134,163,171,181,185},
{0,  1,  6, 17, 21, 57, 75, 83,105,124,138,148,151,176,183,185},
{0,  1,  8, 10, 29, 43, 60, 75, 80,124,128,146,158,169,182,185},
{0,  1,  8, 13, 39, 66, 68, 90,101,122,137,162,165,171,181,185},
{0,  1, 11, 28, 31, 66, 71, 80,122,124,148,156,163,169,181,185},
{0,  1, 12, 14, 31, 36, 52, 56,101,110,138,144,167,170,177,185},
{0,  1, 12, 16, 38, 48, 57,101,118,125,131,152,160,180,183,185},
{0,  1, 12, 27, 37, 45, 69, 76, 92,122,142,163,176,180,182,185},
{0,  1, 13, 16, 23, 44, 55, 69, 95,114,144,152,161,179,181,185},
{0,  1, 14, 18, 30, 68, 79, 87,102,123,143,145,150,176,182,185},
{0,  1, 14, 18, 34, 59, 64, 70, 99,107,131,154,173,175,182,185},
{0,  1, 14, 19, 44, 46, 56, 80, 97,108,147,156,162,178,182,185},
{0,  1, 14, 41, 43, 60, 66, 90, 99,110,147,163,173,178,181,185},
{0,  1, 19, 33, 39, 49, 62, 86,103,107,114,149,158,180,183,185},
{0,  2,  3, 15, 35, 72, 83, 91,114,121,130,135,157,175,181,185},
{0,  2,  3, 25, 42, 54, 78, 86,121,135,148,155,166,176,181,185},
{0,  2,  5, 15, 35, 75, 79, 96,120,128,142,151,167,178,179,185},
{0,  2,  5, 25, 33, 54, 60, 67, 84,128,137,147,169,173,184,185},
{0,  2,  5, 27, 36, 71, 78, 82, 99,123,136,146,152,166,184,185},
{0,  2,  7, 13, 21, 44, 62, 71, 72, 97,119,149,153,165,182,185},
{0,  2,  8, 18, 51, 54, 81, 98,109,121,146,159,166,180,181,185},
{0,  2,  8, 21, 31, 32, 76, 96,112,124,129,138,163,178,181,185},
{0,  2,  9, 34, 37, 47, 61, 80,102,110,128,164,168,179,184,185},
{0,  2, 11, 14, 39, 46, 54, 84,104,125,151,161,167,180,184,185},
{0,  2, 12, 18, 25, 40, 61, 72,102,103,129,148,168,177,182,185},
{0,  2, 14, 25, 38, 56, 64, 85,104,107,113,148,165,180,181,185},
{0,  2, 17, 29, 33, 51, 71, 94, 99,129,135,161,174,175,182,185},
{0,  2, 31, 36, 39, 45, 57, 92,103,116,133,143,165,166,181,185},
{0,  3,  5,  9, 22, 43, 63, 93,109,116,140,148,158,173,184,185},
{0,  3,  5, 11, 12, 38, 59, 75, 90,104,114,132,136,155,172,185},
{0,  3,  5, 13, 19, 40, 49, 71, 83,109,124,156,157,174,181,185},
{0,  3,  5, 26, 36, 40, 53, 82,100,112,120,144,163,169,178,185},
{0,  3,  7, 17, 46, 58, 71, 86,105,123,147,149,158,179,180,185},
{0,  3,  7, 23, 29, 38, 77, 88,105,129,139,141,166,171,184,185},
{0,  3,  8, 17, 37, 56, 82, 83,113,124,145,160,167,173,183,185},
{0,  3,  9, 20, 22, 36, 57, 80,104,122,132,147,173,177,178,185},
{0,  3,  9, 35, 40, 42, 62, 83, 98,106,117,155,167,171,184,185},
{0,  3, 10, 11, 24, 50, 56, 86, 91,114,134,152,156,168,183,185},
{0,  3, 10, 12, 31, 54, 78, 86,115,121,126,151,167,171,184,185},
{0,  3, 11, 15, 21, 49, 68, 93,109,126,135,148,149,178,180,185},
{0,  3, 14, 20, 30, 32, 79, 84,103,124,139,146,147,172,181,185},
{0,  3, 16, 27, 39, 57, 61,105,110,125,142,156,175,177,184,185},
{0,  3, 17, 21, 30, 50, 66, 85,108,123,133,145,177,179,184,185},
{0,  3, 18, 23, 42, 76, 88, 90,116,117,125,147,168,172,179,185},
{0,  3, 20, 32, 36, 66, 88,113,114,123,141,164,172,178,183,185},
{0,  4,  5, 19, 26, 39, 64, 76, 87,104,131,134,167,177,183,185},
{0,  4,  5, 20, 37, 72, 78, 81,100,121,129,147,160,171,183,185},
{0,  4,  6,  7, 15, 33, 57, 71, 91,103,119,140,150,163,180,185},
{0,  4,  6, 24, 33, 41, 71, 90,116,130,141,162,169,172,184,185},
{0,  4,  7, 12, 22, 38, 75, 86, 95,119,125,142,144,171,184,185},
{0,  4,  7, 20, 25, 55, 57, 63, 86, 97,125,144,161,170,171,185},
{0,  4,  7, 22, 47, 56, 61, 73, 89,109,153,154,164,177,183,185},
{0,  4,  9, 19, 30, 37, 50, 64, 99,107,131,143,160,182,183,185},
{0,  4, 10, 28, 50, 55, 64, 71, 94,102,113,150,170,182,183,185},
{0,  4, 11, 28, 29, 61, 76,102,114,136,145,166,172,180,182,185},
{0,  4, 13, 18, 29, 41, 62, 72,102,108,150,158,165,182,184,185},
{0,  4, 13, 18, 29, 41, 67, 77, 97,124,132,139,163,182,184,185},
{0,  4, 13, 38, 39, 46, 61, 82,101,106,153,155,165,171,182,185},
{0,  4, 14, 20, 23, 48, 63, 84, 95,117,119,146,172,177,184,185},
{0,  4, 14, 22, 51, 68, 71,109,124,140,149,151,172,179,184,185},
{0,  4, 16, 22, 29, 37, 61, 63,105,114,119,154,157,174,184,185},
{0,  4, 19, 20, 42, 52, 69, 82, 93,128,140,146,149,154,183,185},
{0,  4, 19, 22, 43, 49, 75, 77,106,113,123,160,165,173,174,185},
{0,  5,  6, 27, 36, 38, 62, 80, 99,114,127,139,168,178,182,185},
{0,  5,  7, 36, 37, 50, 59, 76, 92,117,136,164,170,174,182,185},
{0,  5, 11, 26, 29, 45, 57, 89, 93,116,130,155,163,165,172,185},
{0,  5, 12, 14, 43, 44, 62, 84, 99,126,151,159,162,175,179,185},
{0,  5, 22, 35, 45, 66, 82, 94,114,128,152,170,178,179,181,185},
{0,  6,  7, 18, 34, 43, 57, 65, 89,106,110,150,170,180,183,185},
{0,  6,  8, 32, 36, 45, 61, 78, 96,101,144,163,164,175,178,185},
{0,  6, 10, 23, 26, 34, 59, 86,101,123,141,142,171,173,180,185},
{0,  6, 13, 17, 38, 60, 68, 69, 95, 97,109,143,162,167,182,185},
{0,  6, 19, 23, 34, 54, 63, 81, 93,118,119,161,164,169,171,185},
{0,  7,  8, 12, 38, 53, 63, 81,105,128,149,163,165,176,182,185},
{0,  7, 10, 21, 22, 41, 84, 89,107,124,140,149,153,177,179,185},
{0,  7, 16, 22, 41, 65, 73, 85,103,132,145,149,159,180,182,185},
{0,  8, 15, 18, 41, 47, 75, 84,129,133,149,154,171,173,184,185},
{0,  9, 29, 42, 44, 50, 78, 96,110,121,158,161,168,180,184,185},
{0, 11, 12, 20, 25, 62, 72, 79,108,110,136,142,163,166,181,185},
{0, 13, 20, 22, 30, 55, 69, 92, 96,128,140,156,159,174,180,185},
{0, 13, 30, 49, 53, 71, 81, 95,110,126,147,173,174,180,182,185},
{0, 14, 15, 24, 41, 60, 88, 99,122,128,130,160,165,178,181,185},
{0, 14, 16, 21, 24, 66, 67, 92,104,122,131,151,162,166,179,185},

},