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\n A Steiner triple system of order\n \n \n \n v<\/mml:mi>\n v<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , an STS(\n \n \n \n v<\/mml:mi>\n v<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ), is a set of\n \n \n \n 3<\/mml:mn>\n 3<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -element subsets, called blocks, of a\n \n \n \n v<\/mml:mi>\n v<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -element set of points, such that every pair of distinct points occurs in exactly one block. A subsystem of order\n \n \n \n w<\/mml:mi>\n w<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n in an STS(\n \n \n \n v<\/mml:mi>\n v<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ), a sub-STS(\n \n \n \n w<\/mml:mi>\n w<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ), is a subset of blocks that forms an STS(\n \n \n \n w<\/mml:mi>\n w<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ). Constructive and nonconstructive techniques for enumerating up to isomorphism the STS(\n \n \n \n v<\/mml:mi>\n v<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ) that admit at least one sub-STS(\n \n \n \n w<\/mml:mi>\n w<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ) are presented here for general parameters\n \n \n \n v<\/mml:mi>\n v<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and\n \n \n \n w<\/mml:mi>\n w<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . The techniques are further applied to show that the number of isomorphism classes of STS(\n \n \n \n 21<\/mml:mn>\n 21<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n )s with at least one sub-STS(\n \n \n \n 9<\/mml:mn>\n 9<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ) is\n \n \n \n 12661527336<\/mml:mn>\n 12661527336<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and of STS(\n \n \n \n 27<\/mml:mn>\n 27<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n )s with a sub-STS(\n \n \n \n 13<\/mml:mn>\n 13<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ) is\n \n \n \n 1356574942538935943268083236<\/mml:mn>\n 1356574942538935943268083236<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/mcom\/2945","type":"journal-article","created":{"date-parts":[[2015,4,7]],"date-time":"2015-04-07T10:56:21Z","timestamp":1428404181000},"page":"3051-3067","source":"Crossref","is-referenced-by-count":5,"title":["Enumeration of Steiner triple systems with subsystems"],"prefix":"10.1090","volume":"84","author":[{"given":"Petteri","family":"Kaski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patric","family":"\u00d6sterg\u00e5rd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandru","family":"Popa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,4,7]]},"reference":[{"issue":"7","key":"1","doi-asserted-by":"publisher","first-page":"1414","DOI":"10.1016\/j.jcta.2012.03.013","article-title":"On triple systems and strongly regular graphs","volume":"119","author":"Behbahani, Majid","year":"2012","journal-title":"J. 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