I'm trying to find a $6\times k$ binary matrix over $\mathbb R$ such that
- Each row contains $t$ ones and rest enteries are zeroes.
- Sum of any $5$ rows contains atleast $2t$ non zeroes.
- Sum of any $4$ rows contains atmost $2t-1$ non zeros.
While a direct solution is acceptable, I'm looking for the method on how to find, prefereably, expressing it in linear algebraic terms somehow and then solving it