Bounds table.

Summary comparison of several upper and lower bounds. Gr&M refers to Groeneveld and Meeden 1977 [11], C&R refers to Chen and Rubin 1986 [4], B&P refers to Berg and Pedersen 2006 [6], and Ga&M refers to Gaunt and Merkle 2021 [3]. The * refers to bounds presented with informal proofs or derivations, and ** for bounds presented as conjectures without proof, in Lyon 2021 [1]; in the present paper they are treated as new theorems, with proofs.

若干上下界的汇总对比。其中Gr&M指代1977年Groeneveld与Meeden的研究文献[11]，C&R指代1986年Chen与Rubin的研究文献[4]，B&P指代2006年Berg与Pedersen的研究文献[6]，Ga&M指代2021年Gaunt与Merkle的研究文献[3]。在Lyon 2021年的研究文献[1]中，符号*代表带有非形式化证明或推导的界，符号**代表仅作为猜想未给出正式证明的界；而在本文中，此类界被视为全新定理，并补充了完整证明过程。