; or (B) in any region in which local educational agencies may not have a sufficient elementary school and secondary school student population to support the placement of all participating graduate students, a partnership between a State educational agency, on behalf of 1 or more low-income local educational agencies, and 1 or more eligible graduate institutions. (4) Institution of higher education The term institution of higher education has the meaning given such term in section 102 of the Higher Education Act of 1965 ( 20 U.S.C. 1002 ), but excludes any institution of higher education described in section 102(a)(1)(C) of such Act. (5) Local educational agency (A) In general The term local educational agency means a public board of education or other public authority legally constituted within a State for either administrative control or direction of, or to perform a service function for, public elementary schools or secondary schools in a city, county, township, school district, or other political subdivision of a State, or of or for a combination of school districts or counties that is recognized in a State as an administrative agency for its public elementary schools or secondary schools. (B) Administrative control and direction The term includes any other public institution or agency having administrative control and direction of a public elementary school or secondary school. (C) Bureau of Indian Education schools The term includes an elementary school or secondary school funded by the Bureau of Indian Education but only to the extent that including the school makes the school eligible for programs for which specific eligibility is not provided to the school in another provision of law and the school does not have a student population that is smaller than the student population of the local educational agency receiving assistance under this Act with the smallest student population, except that the school shall not be subject to the jurisdiction of any State educational agency other than the Bureau of