description of files
--------------------

below_1018_padic_saved.txt: 72306 triples with c < 10^18
above_1018_padic_saved.txt: 33947 triples with c > 10^18 but < 2^63
specialcases_padic.txt:       371 triples from three sources: 
                            high quality, high merit, unbeaten triples

see paper for terminology

explanation of abbreviations
----------------------------

deg:  approximation degree 
rag:  real approximation gain 
rpg:  real power gain 
rd:   real approximation degree
spag: strict p-adic approximation gain 
sppg: strict p-adic power gain 
sd:   strict p-adic approximation degree
mpag: multiple p-adic approximation gain 
mppg: multiple p-adic power gain 
md:   multiple approximation degree

counter refers to the line number in Bart de Smit's files

selection criteria
------------------
c < 10^18 :             rag > 1.10   or spag > 1.31  or mpag > 1.37
                     or rpg > 2.66   or sppg > 1.90  or mppg > 1.57
                     or rd >= 43     or sd >= 43     or md >= 43 
                     or sp > 250M    or mpag < rag
10^18 < c < 2^63 :      rag > 0.90   or spag > 1.02  or mpag > 1.09
                     or rpg > 2.45   or sppg > 1.86  or mppg > 1.51
                     or rd >= 50     or sd >= 50     or md >= 50 
                     or sp > 10000M  or mpag < rag
special cases: only c > 2^63, undoubled