Best Known (86−71, 86, s)-Nets in Base 9
(86−71, 86, 64)-Net over F9 — Constructive and digital
Digital (15, 86, 64)-net over F9, using
- t-expansion [i] based on digital (13, 86, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
(86−71, 86, 299)-Net in Base 9 — Upper bound on s
There is no (15, 86, 300)-net in base 9, because
- 4 times m-reduction [i] would yield (15, 82, 300)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(982, 300, S9, 67), but
- the linear programming bound shows that M ≥ 7 902952 737901 271843 431889 735617 226351 187571 898753 628713 991780 519430 985447 654185 791444 354088 298900 446645 515048 296642 656855 056762 309661 063423 734597 540445 775144 567234 367121 860943 493961 811499 254778 735889 984375 / 4 360409 577793 881679 952067 707020 893702 448546 638866 206202 354682 760284 986661 689674 184257 068519 240808 049889 963460 421015 382230 155831 > 982 [i]
- extracting embedded orthogonal array [i] would yield OA(982, 300, S9, 67), but