Elementary or secondary school means a not-for-profit educational institution located within this state which is not owned or controlled by the state or any political subdivision, agency, instrumentality, district, or municipality thereof, which is authorized by law to provide a program of education which:

(1) Is for any or all of the grades kindergarten through twelfth grade;

(2) Is approved or accredited by the State Department of Education; and

(3) Does not discriminate in the admission of students on the basis of race, color, creed, national origin, ancestry, age, sex, or handicap, except that nothing in the Nebraska Elementary and Secondary School Finance Authority Act shall be construed or interpreted to prohibit the authority from financing a project for any elementary or secondary school which admits only students of a single gender.