Best Known (18, 18+76, s)-Nets in Base 8
(18, 18+76, 65)-Net over F8 — Constructive and digital
Digital (18, 94, 65)-net over F8, using
- t-expansion [i] based on digital (14, 94, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(18, 18+76, 299)-Net in Base 8 — Upper bound on s
There is no (18, 94, 300)-net in base 8, because
- 4 times m-reduction [i] would yield (18, 90, 300)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(890, 300, S8, 72), but
- the linear programming bound shows that M ≥ 10399 854705 888883 107854 305204 007404 408362 367511 093302 641670 587633 388156 360358 919981 201961 486046 614211 212601 895183 975675 730166 486292 444589 667989 826301 822518 449736 306010 709693 647642 677990 101446 116800 689569 062081 216428 138976 082903 403134 827521 638400 000000 / 4 971137 993580 037247 820859 317840 581529 140389 218119 836472 693535 724813 803850 022567 036632 869015 066631 388220 568436 373891 181619 607410 318341 993524 706207 810789 292558 557231 002671 > 890 [i]
- extracting embedded orthogonal array [i] would yield OA(890, 300, S8, 72), but