Block-Transitive 3-(v, 5, λ) Designs with Sporadic or Alternating Socle

Key Points

• All classified 3-designs feature a block size of 5, enriching the understanding of their properties.
• Sporadic simple groups and alternating groups play crucial roles in the classification of these designs.
• Using group theory, we explored transitive actions on blocks, defining their socle structures.
• Highlights the complexities of block-transitive designs, suggesting future research directions into group actions.