New infinite families of 3-designs from algebraic curves over FqFq

In this paper, we show that the stabilizer subgroup of Df+={a∈Fq|f(a)∈(Fq×)2} for a f∈Fq[x]f∈Fq[x] without multiple roots can be derived from the stabilizer of Df0={a∈F¯q|f(a)=0}∪{∞}. As an application, we construct a family of 3-designs such as 3−(q+1,q−12,(q−1)(q−3)(q−5)16), where qq is a prime power such that q≡3(mod4) and q≥59q≥59.