Best Known (51−41, 51, s)-Nets in Base 9
(51−41, 51, 40)-Net over F9 — Constructive and digital
Digital (10, 51, 40)-net over F9, using
- t-expansion [i] based on digital (8, 51, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(51−41, 51, 54)-Net over F9 — Digital
Digital (10, 51, 54)-net over F9, using
- net from sequence [i] based on digital (10, 53)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 10 and N(F) ≥ 54, using
(51−41, 51, 234)-Net in Base 9 — Upper bound on s
There is no (10, 51, 235)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(951, 235, S9, 41), but
- the linear programming bound shows that M ≥ 2 848880 717187 902127 983030 032262 388466 820408 074764 158910 574332 029568 594494 136301 038752 852370 981154 251600 / 595894 630941 027491 427276 782542 936823 246172 808085 753773 > 951 [i]