=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= f11 1 3 5 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= f11 f12 f22 1 0 1 1 0 2 1 0 3 1 0 5 2 0 3 2 2 3 3 0 3 ------------------------- 1 0 4 borderline 2 2 5 borderline 3 2 3 borderline =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= disc: f11 f22 f33 f23 f13 f12 succeed 4: 1 1 1 0 0 0 succeed 8: 1 1 2 0 0 0 succeed 12: 1 1 3 0 0 0 succeed 12: 1 2 2 2 0 0 succeed 20: 1 1 5 0 0 0 succeed 20: 1 2 3 2 0 0 succeed 24: 1 2 3 0 0 0 succeed 28: 2 2 3 2 2 2 succeed 36: 1 2 5 2 0 0 succeed 36: 1 3 3 0 0 0 succeed 36: 2 2 3 0 0 2 succeed 60: 2 3 3 0 0 2 ----------------------------------------------------------- succeed 16: 1 1 4 0 0 0 borderline succeed 16: 1 2 2 0 0 0 borderline succeed 32: 1 3 3 2 0 0 borderline succeed 32: 2 2 3 2 2 0 borderline succeed 48: 2 3 3 2 2 2 borderline succeed 64: 3 3 3 -2 2 2 borderline =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= disc: f11 f22 f33 f44 f12 f13 f23 f14 f24 f34 succeed 16: 1 1 1 1 0 0 0 0 0 0 succeed 32: 1 1 1 2 0 0 0 0 0 0 succeed 48: 1 1 1 3 0 0 0 0 0 0 succeed 48: 1 1 2 2 0 0 0 0 0 2 succeed 80: 1 1 2 3 0 0 0 0 0 2 succeed 96: 1 1 2 3 0 0 0 0 0 0 succeed 112: 1 2 2 3 0 0 2 0 2 0 succeed 144: 1 1 2 5 0 0 0 0 0 2 succeed 144: 1 2 2 3 0 0 2 0 0 0 succeed 240: 2 2 3 3 2 2 0 2 0 0 succeed 240: 1 2 3 3 0 0 0 0 2 0 ----------------------------------------------------------- succeed 64: 1 1 1 4 0 0 0 0 0 0 borderline succeed 64: 1 1 2 2 0 0 0 0 0 0 borderline succeed 64: 1 2 2 2 0 0 2 0 2 0 borderline succeed 80: 1 1 1 5 0 0 0 0 0 0 borderline succeed 128: 1 1 3 3 0 0 0 0 0 2 borderline succeed 128: 1 2 2 3 0 0 0 0 2 2 borderline succeed 128: 2 2 2 3 2 2 0 2 0 0 borderline succeed 144: 1 1 3 3 0 0 0 0 0 0 borderline succeed 192: 1 2 3 3 0 0 2 0 2 0 borderline succeed 192: 2 2 2 3 0 0 0 2 2 2 borderline succeed 256: 1 3 3 3 0 0 2 0 2 -2 borderline succeed 256: 2 2 3 3 0 2 2 2 2 2 borderline succeed 256: 2 2 3 3 2 2 0 0 2 0 borderline succeed 304: 2 2 3 3 0 2 2 0 2 0 borderline succeed 512: 3 3 3 3 2 2 -2 -2 -2 2 borderline =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= disc: f11 f22 f33 f44 f55 f12 f13 f23 f14 f24 f34 f15 f25 f35 f45 succeed 16: 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 succeed 32: 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 succeed 48: 1 1 1 1 3 0 0 0 0 0 0 0 0 0 0 succeed 48: 1 1 1 2 2 0 0 0 0 0 0 0 0 0 2 succeed 80: 1 1 1 2 3 0 0 0 0 0 0 0 0 0 2 succeed 112: 1 1 2 2 3 0 0 0 0 0 2 0 0 2 0 succeed 144: 1 1 2 2 3 0 0 0 0 0 2 0 0 0 0 ----------------------------------------------------------- succeed 64: 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 borderline succeed 64: 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 borderline succeed 64: 1 1 2 2 2 0 0 0 0 0 2 0 0 0 2 borderline succeed 64: 1 2 2 2 2 0 0 0 0 0 0 0 2 2 2 borderline succeed 96: 1 1 1 2 3 0 0 0 0 0 0 0 0 0 0 borderline succeed 112: 1 1 1 2 4 0 0 0 0 0 0 0 0 0 2 borderline succeed 128: 1 1 1 3 3 0 0 0 0 0 0 0 0 0 2 borderline succeed 128: 1 1 2 2 3 0 0 0 0 0 0 0 0 2 2 borderline succeed 128: 1 2 2 2 3 0 0 2 0 2 0 0 2 0 0 borderline succeed 144: 1 2 2 2 3 0 0 2 0 2 0 0 0 0 2 borderline succeed 144: 1 1 1 2 5 0 0 0 0 0 0 0 0 0 2 borderline succeed 160: 1 1 2 2 3 0 0 0 0 0 0 0 0 0 2 borderline succeed 192: 1 1 2 3 3 0 0 0 0 0 2 0 0 2 0 borderline succeed 192: 1 2 2 2 3 0 0 0 0 0 0 0 2 2 2 borderline succeed 208: 1 1 2 3 3 0 0 0 0 0 0 0 0 2 2 borderline succeed 240: 1 1 2 3 3 0 0 0 0 0 2 0 0 0 0 borderline succeed 256: 1 1 3 3 3 0 0 0 0 0 2 0 0 2 -2 borderline succeed 256: 1 2 2 3 3 0 0 0 0 2 2 0 2 2 2 borderline succeed 256: 1 2 2 3 3 0 0 2 0 2 0 0 0 2 0 borderline succeed 256: 2 2 2 2 3 0 0 0 0 0 0 2 2 2 2 borderline succeed 256: 2 2 2 3 3 2 2 0 2 0 0 2 0 0 2 borderline =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= must wonder whether there is a dimension 5 odd lattice generated by vectors of norm 3, determinant as integral matrix could be 64, so Nipp's discriminant should be 1024. If so, how well does it do with this hybrid covering radius condition? Answer: not well. jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ ./read_some_lines_from_nipp_5 3 3 3 3 3 2 2 2 -2 -2 2 -2 -2 -2 2 WORSE 1 4 4 0 1 testing 1024: 3 3 3 3 3 2 2 2 -2 -2 2 -2 -2 -2 2 fail 1 global 0 so, bad behavior at point ( 1/8, 1/2, 1/2, 0, 1/8) 3 1 1 -1 -1 1 3 1 -1 -1 1 1 3 1 -1 -1 -1 1 3 1 -1 -1 -1 1 3 jagy@phobeusjunior:~$ gp Reading GPRC: /etc/gprc ...Done. GP/PARI CALCULATOR Version 2.3.4 (released) ? m5 = [ 3, 1, 1, -1, -1; 1, 3, 1, -1, -1; 1, 1, 3, 1, -1;-1, -1, 1, 3, 1;-1, -1, -1, 1, 3] %17 = [3 1 1 -1 -1] [1 3 1 -1 -1] [1 1 3 1 -1] [-1 -1 1 3 1] [-1 -1 -1 1 3] ? m5 - mattranspose(m5) %18 = [0 0 0 0 0] [0 0 0 0 0] [0 0 0 0 0] [0 0 0 0 0] [0 0 0 0 0] ? matdet(m5) %19 = 64 ? ? charpoly(m5) %20 = x^5 - 15*x^4 + 80*x^3 - 188*x^2 + 192*x - 64 ? ? factor( charpoly(m5) ) %22 = [x - 4 1] [x - 2 2] [x^2 - 7*x + 4 1] ? =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=