The Massachusetts School Building Authority’s board of directors has authorized the town to enter into the “invitation to eligibility” period for Billerica Memorial High School, This is the first step in a process that may lead to a high school construction project, according to School Superintendent Timothy Piwowar. The School Building Authority board’s unanimous Jan. 29 vote was based on its review of the district’s statement of interest in a high school project, which was filed in April 2013. The 270-day eligibility period is a prerequisite to a School Building Authority vote to authorize a feasibility study. During the eligibility period, the authority will work with the school district to determine its financial and community readiness to construct a new school, according to a statement released by state Treasurer Steven Grossman, authority chairman. If Billerica successfully completes the eligibility period requirements, the district would become eligible for the feasibility study phase of the process. Billerica Town Meeting in November approved establishment of a 16-member high school building committee and appropriation of $2 million for a feasibility study of the high school, which opened in 1955.