Best Known (109−78, 109, s)-Nets in Base 5
(109−78, 109, 72)-Net over F5 — Constructive and digital
Digital (31, 109, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
(109−78, 109, 298)-Net in Base 5 — Upper bound on s
There is no (31, 109, 299)-net in base 5, because
- 2 times m-reduction [i] would yield (31, 107, 299)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5107, 299, S5, 76), but
- 1 times code embedding in larger space [i] would yield OA(5108, 300, S5, 76), but
- the linear programming bound shows that M ≥ 172 017384 805704 886566 668130 771081 911232 285722 070421 968211 093096 009064 930352 517220 406582 146762 560038 183476 563586 847091 389217 297972 623089 013577 114021 476755 230182 061165 902269 682980 765727 726776 666229 825015 446453 579896 898923 249136 731778 812063 165429 681516 928328 566251 593656 488694 250583 648681 640625 / 40199 997011 471819 313842 150832 888431 440114 882676 318816 079816 062906 513709 507675 739139 909459 671628 190057 296570 577398 147635 345097 078652 726129 720344 129591 183425 466480 139020 430090 292379 961116 039444 189830 924416 825213 949409 > 5108 [i]
- 1 times code embedding in larger space [i] would yield OA(5108, 300, S5, 76), but
- extracting embedded orthogonal array [i] would yield OA(5107, 299, S5, 76), but