{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:49:39Z","timestamp":1761752979356,"version":"build-2065373602"},"reference-count":0,"publisher":"University of Calgary","issue":"2","license":[{"start":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:00:00Z","timestamp":1761609600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Contrib Discrete Math"],"abstract":"<jats:p>Consider a hyperbolic or an elliptic quadric $Q^\\epsilon(3,q)$, $\\epsilon \\in \\{ +,- \\}$, in $\\operatorname{PG}(3,q)$ and let $\\mathcal{E}^\\epsilon$ denote the set of all lines of $\\operatorname{PG}(3,q)$ that are external with respect to $Q^\\epsilon(3,q)$. If $\\pi$ is a (tangent or secant) plane of $\\operatorname{PG}(3,q)$, then $\\pi \\setminus Q^\\epsilon(3,q)$ is an $\\mathcal{E}^\\epsilon$-blocking set which is minimal, except when $(q,\\epsilon) = (2,+)$ and $\\pi$ is a secant plane. In this way, we obtain two families of (minimal) blocking sets of sizes $m_1^\\epsilon$ and $m_2^\\epsilon$, with $(m_1^+,m_2^+)=(q^2-q,q^2)$ and $(m_1^-,m_2^-)=(q^2,q^2+q)$, where those of size $m_1^\\epsilon$ are also the minimum size $\\mathcal{E}^\\epsilon$-blocking sets. Motivated by the search for new (families of) minimal $\\mathcal{E}^\\epsilon$-blocking sets with sizes in the open interval $]m_1^\\epsilon,m_2^\\epsilon[$, we determine here all $\\mathcal{E}^\\epsilon$-blocking sets of size $m_1^\\epsilon+1$ in $\\operatorname{PG}(3,q)$ in the case $q \\in \\{ 2,3 \\}$.<\/jats:p>","DOI":"10.55016\/ojs\/cdm.v20i2.73655","type":"journal-article","created":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:46:33Z","timestamp":1761752793000},"page":"200-218","source":"Crossref","is-referenced-by-count":0,"title":["On next-to-minimum size blocking sets of external lines to a nondegenerate quadric in $\\operatorname{PG}(3,q)$"],"prefix":"10.55016","volume":"20","author":[{"given":"Bart","family":"De Bruyn","sequence":"first","affiliation":[]},{"given":"Puspendu","family":"Pradhan","sequence":"additional","affiliation":[]},{"given":"Binod Kumar","family":"Sahoo","sequence":"additional","affiliation":[]}],"member":"13844","published-online":{"date-parts":[[2025,10,28]]},"container-title":["Contributions to Discrete Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/73655\/58514","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/73655\/58514","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:46:34Z","timestamp":1761752794000},"score":1,"resource":{"primary":{"URL":"https:\/\/cdm.ucalgary.ca\/article\/view\/73655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,28]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,10,28]]}},"URL":"https:\/\/doi.org\/10.55016\/ojs\/cdm.v20i2.73655","relation":{},"ISSN":["1715-0868"],"issn-type":[{"value":"1715-0868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,28]]}}}