{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T21:40:23Z","timestamp":1773870023239,"version":"3.50.1"},"reference-count":12,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:00:00Z","timestamp":1773792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401326"],"award-info":[{"award-number":["12401326"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper proposes a blocked individual aliased effect number pattern (BI-AENP) for regular blocked designs and establishes its relationships with the core patterns of several existing optimality criteria. We develop an algorithm to compute the BI-AENP. A catalogue of 16-, 32-, and 64-run BI-AENP 2n\u2212k:2r designs is presented, together with comparisons with the minimum aberration and clear effects criteria.<\/jats:p>","DOI":"10.3390\/e28030340","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T14:14:05Z","timestamp":1773843245000},"page":"340","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Blocked Two-Level Regular Designs with Individual Aliased Effect Number Pattern"],"prefix":"10.3390","volume":"28","author":[{"given":"Min","family":"Han","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1581-9727","authenticated-orcid":false,"given":"Shengli","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hedayat, A.S., Sloane, N.J.A., and Stufken, J. (1999). Orthogonal Arrays: Theory and Applications, Springer.","DOI":"10.1007\/978-1-4612-1478-6"},{"key":"ref_2","unstructured":"Mukerjee, R., and Wu, C.F.J. (2006). A Modern Theory of Factorial Design, Springer."},{"key":"ref_3","first-page":"298","article-title":"Optimal Blocking Schemes for 2n and 2n\u2212p Designs","volume":"39","author":"Sun","year":"1997","journal-title":"Technometrics"},{"key":"ref_4","unstructured":"Wu, C.F.J., and Hamada, M. (2000). Experiments: Planning, Analysis and Parameter Design Optimization, Wiley."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1948","DOI":"10.1214\/aos\/1017939246","article-title":"Theory of optimal blocking of 2n\u2212m designs","volume":"27","author":"Chen","year":"1999","journal-title":"Ann. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1198\/004017002188618455","article-title":"Choice of optimal blocking schemes in two-level and three-level designs","volume":"44","author":"Cheng","year":"2002","journal-title":"Technometrics"},{"key":"ref_7","first-page":"382","article-title":"Fractional resolution and minimum aberration in blocked 2n\u2212k designs","volume":"39","author":"Sitter","year":"1997","journal-title":"Technometrics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0378-3758(00)00133-6","article-title":"Optimal blocking of two-level fractional factorial designs","volume":"91","author":"Zhang","year":"2000","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4436","DOI":"10.1016\/j.jspi.2005.07.006","article-title":"Some results on blocked regular two-level fractional factorial designs with clear effects","volume":"136","author":"Chen","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1080\/15598608.2014.840517","article-title":"Blocked two-level regular designs with general minimum lower order confounding","volume":"8","author":"Wei","year":"2014","journal-title":"J. Stat. Theory Pract."},{"key":"ref_11","first-page":"1787","article-title":"General minimum lower order confounding in block designs using complementary sets","volume":"19","author":"Zhang","year":"2009","journal-title":"Statist. Sin."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106316","DOI":"10.1016\/j.jspi.2025.106316","article-title":"Individual aliased effect number pattern for two-level designs and its applications","volume":"241","author":"Zhao","year":"2026","journal-title":"J. Stat. Plan. Inference"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/340\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T14:18:50Z","timestamp":1773843530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/340"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,18]]},"references-count":12,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["e28030340"],"URL":"https:\/\/doi.org\/10.3390\/e28030340","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,18]]}}}