tt-wise balanced designs

Steiner 3-wise balanced designs are constructed for parameters 3-(3n−1,{4,8},1)(3n−1,{4,8},1), 3-(qnm−qm,{q−1,q,q+1},1)(qnm−qm,{q−1,q,q+1},1), 3-(qnm−2qm−1,{qm−3,qm−2,qm−1,qm,qm+1},1)(qnm−2qm−1,{qm−3,qm−2,qm−1,qm,qm+1},1), 3-(qnm−2qm,{qm−3,qm−2,qm−1,qm,qm+1},1)(qnm−2qm,{qm−3,qm−2,qm−1,qm,qm+1},1), 3-(qnm−2qm+1,{qm−3,qm−2,qm−1,qm,qm+1},1)(qnm−2qm+1,{qm−3,qm−2,qm−1,qm,qm+1},1), where qq is a prime power and n≥2,m≥1 are integers. Further designs are obtained from these.