{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:38:04Z","timestamp":1776724684251,"version":"3.51.2"},"reference-count":7,"publisher":"American Mathematical Society (AMS)","issue":"221","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    It is proved that there are precisely 4204 pairwise non-isomorphic Steiner systems\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S left-parenthesis 5 comma 6 comma 72 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>6<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>72<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">S(5,6,72)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    invariant under the group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper P normal upper S normal upper L Subscript 2 Baseline left-parenthesis 71 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">P<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">S<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">L<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>71<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathrm {PSL}_2(71)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and which can be constructed using only short orbits. It is further proved that there are precisely 38717 pairwise non-isomorphic Steiner systems\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S left-parenthesis 5 comma 6 comma 84 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>6<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>84<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">S(5,6,84)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    invariant under the group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper P normal upper S normal upper L Subscript 2 Baseline left-parenthesis 83 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">P<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">S<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">L<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>83<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathrm {PSL}_2(83)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and which can be constructed using only short orbits.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00924-7","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"357-359","source":"Crossref","is-referenced-by-count":7,"title":["Steiner systems \ud835\udc46(5,6,\ud835\udc63) with \ud835\udc63=72 and 84"],"prefix":"10.1090","volume":"67","author":[{"given":"M.","family":"Grannell","sequence":"first","affiliation":[]},{"given":"T.","family":"Griggs","sequence":"additional","affiliation":[]},{"given":"R.","family":"Mathon","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1112\/blms\/8.3.263","article-title":"Some new 5-designs","volume":"8","author":"Denniston, R. H. F.","year":"1976","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"2","first-page":"45","article-title":"A note on the Steiner systems \ud835\udc46(5,6,24)","volume":"8","author":"Grannell, M. J.","year":"1979","journal-title":"Ars Combin.","ISSN":"https:\/\/id.crossref.org\/issn\/0381-7032","issn-type":"print"},{"key":"3","first-page":"77","article-title":"On Steiner systems \ud835\udc46(5,6,48)","volume":"12","author":"Grannell, M. J.","year":"1992","journal-title":"J. Combin. Math. Combin. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0835-3026","issn-type":"print"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1002\/jcd.3180010304","article-title":"Some Steiner 5-designs with 108 and 132 points","volume":"1","author":"Grannell, M. J.","year":"1993","journal-title":"J. Combin. Des.","ISSN":"https:\/\/id.crossref.org\/issn\/1063-8539","issn-type":"print"},{"key":"5","first-page":"193","article-title":"A new 5-design","volume":"6","author":"Mills, W. H.","year":"1978","journal-title":"Ars Combin.","ISSN":"https:\/\/id.crossref.org\/issn\/0381-7032","issn-type":"print"},{"issue":"41","key":"6","first-page":"164","article-title":"\ud835\udc61-Designs zu vorgegebener Automorphismengruppe","author":"Schmalz, Bernd","year":"1992","journal-title":"Bayreuth. Math. Schr.","ISSN":"https:\/\/id.crossref.org\/issn\/0172-1062","issn-type":"print"},{"key":"7","doi-asserted-by":"crossref","unstructured":"E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg 12 (1938), 256\u2013264.","DOI":"10.1007\/BF02948947"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00924-7\/S0025-5718-98-00924-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00924-7\/S0025-5718-98-00924-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:41:28Z","timestamp":1776721288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00924-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":7,"journal-issue":{"issue":"221","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["S0025-5718-98-00924-7"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-98-00924-7","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1998]]}}}