Some Lower Bounds

any deterministic C ≥ 2 McGeoch et al
any memoryless C ≥ 2 McGeoch et al
line   C ≥ 1 + e-1/2 ≈ 1.6065 Chrobak et al
general trackless deterministic C ≥ 23/11 Bein et al
general trackless C ≥ 1 + √2/2 Bein et al
uniform   C ≥ 3/2 Fiat, Karp, et al
uniform trackless C ≥ 8453/5458 ≈ 1.548735 Bein et al