The initial degree of symbolic powers of Fermat-like ideals of planes and lines arrangements

We explicitly compute the least degree of generators all symbolic powers defining ideal Fermat-like configuration lines in PC3, except for second powers, where we provide bounds them. will also those numbers determining singular locus arrangement given by pseudoreflection group A3. As direct applications, verify Chudnovsky’s(-like) Conjecture, Demailly’s(-like) Conjecture and Harbourne-Huneke Containment problem as well calculate Waldschmidt constant (asymptotic) resurgence number.