Some important classes of neighbor balanced designs in linear blocks of small sizes

Neighbor balanced designs are useful to balance out the neighbor effects in field of agriculture, serology, agro forestry, industry, etc. In most of the agriculture experiments blocks are formed in a line and therefore, neighbor balanced designs are required in linear blocks. In this article some classes of first order neighbor balanced designs are presented in linear blocks of size three and four. A method to construct the second order neighbor balanced designs through two minimal first order neighbor balanced designs in linear binary blocks of size three is also developed here.