{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:38:09Z","timestamp":1776800289517,"version":"3.51.2"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"300","license":[{"start":{"date-parts":[[2017,1,7]],"date-time":"2017-01-07T00:00:00Z","timestamp":1483747200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we introduce a novel approach to searching for rank-1 lattice rules. The idea is to separate the search into two steps, first finding good generating vectors and then finding the corresponding optimal\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N\">\n                        <mml:semantics>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    value. For the trigonometric degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"delta equals 5\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03b4\n                              \n                            <\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\delta = 5<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    we establish a simple criterion on the generating vectors. By using the theory for Golomb rulers and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper B 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">B<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">{\\mathcal B}_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -series we construct efficient algorithms for finding good generating vectors. Combined with our own home-brewed algorithm for finding the corresponding optimal\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N\">\n                        <mml:semantics>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , we produce new good rank-1 lattice rules of high dimension.\n                  <\/p>","DOI":"10.1090\/mcom3047","type":"journal-article","created":{"date-parts":[[2015,2,25]],"date-time":"2015-02-25T10:40:20Z","timestamp":1424860820000},"page":"1821-1835","source":"Crossref","is-referenced-by-count":0,"title":["Good low degree rank-1 lattice rules of high dimension"],"prefix":"10.1090","volume":"85","author":[{"given":"Tor","family":"S\u00f8revik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2016,1,7]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/BF02566968","article-title":"Theorems in the additive theory of numbers","volume":"37","author":"Bose, R. 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